diff --git a/docs/harfbuzz-sections.txt b/docs/harfbuzz-sections.txt
index 9263994b0..f81058b53 100644
--- a/docs/harfbuzz-sections.txt
+++ b/docs/harfbuzz-sections.txt
@@ -537,6 +537,7 @@ hb_ot_layout_feature_with_variations_get_lookups
 hb_ot_layout_get_attach_points
 hb_ot_layout_get_horizontal_baseline_tag_for_script
 hb_ot_layout_get_baseline
+hb_ot_layout_get_baseline_with_fallback
 hb_ot_layout_get_glyph_class
 hb_ot_layout_get_glyphs_in_class
 hb_ot_layout_get_ligature_carets
diff --git a/src/hb-ot-layout.cc b/src/hb-ot-layout.cc
index aaabc687d..0d556aa5b 100644
--- a/src/hb-ot-layout.cc
+++ b/src/hb-ot-layout.cc
@@ -1979,6 +1979,7 @@ hb_ot_layout_substitute_lookup (OT::hb_ot_apply_context_t *c,
 hb_ot_layout_baseline_tag_t
 hb_ot_layout_get_horizontal_baseline_tag_for_script (hb_script_t script)
 {
+  /* Keep in sync with hb_ot_layout_get_baseline_with_fallback */
   switch ((int) script)
   {
     /* Unicode-1.1 additions */
@@ -2043,7 +2044,7 @@ hb_ot_layout_get_horizontal_baseline_tag_for_script (hb_script_t script)
  * @direction: text direction.
  * @script_tag:  script tag.
  * @language_tag: language tag, currently unused.
- * @coord: (out): baseline value if found.
+ * @coord: (out) (nullable): baseline value if found.
  *
  * Fetches a baseline value from the face.
  *
@@ -2066,6 +2067,187 @@ hb_ot_layout_get_baseline (hb_font_t                   *font,
 
   return result;
 }
+
+/**
+ * hb_ot_layout_get_baseline_with_fallback:
+ * @font: a font
+ * @baseline_tag: a baseline tag
+ * @direction: text direction.
+ * @script_tag:  script tag.
+ * @language_tag: language tag, currently unused.
+ * @coord: (out): baseline value if found.
+ *
+ * Fetches a baseline value from the face, and synthesizes
+ * it if the font does not have it.
+ *
+ * Since: REPLACEME
+ **/
+void
+hb_ot_layout_get_baseline_with_fallback (hb_font_t                   *font,
+					 hb_ot_layout_baseline_tag_t  baseline_tag,
+					 hb_direction_t               direction,
+					 hb_tag_t                     script_tag,
+					 hb_tag_t                     language_tag,
+					 hb_position_t               *coord /* OUT */)
+{
+  if (hb_ot_layout_get_baseline (font,
+                                 baseline_tag,
+                                 direction,
+                                 script_tag,
+                                 language_tag,
+                                 coord))
+    return;
+
+  /* Synthesize missing baselines.
+   * See https://www.w3.org/TR/css-inline-3/#baseline-synthesis-fonts
+   */
+  switch (baseline_tag)
+  {
+  case HB_OT_LAYOUT_BASELINE_TAG_ROMAN:
+    *coord = 0; // FIXME origin ?
+    break;
+
+  case HB_OT_LAYOUT_BASELINE_TAG_MATH:
+    {
+      hb_codepoint_t glyph;
+      hb_glyph_extents_t extents;
+      if (HB_DIRECTION_IS_HORIZONTAL (direction) &&
+          (hb_font_get_nominal_glyph (font, 0x2212u, &glyph) ||
+           hb_font_get_nominal_glyph (font, '-', &glyph)) &&
+          hb_font_get_glyph_extents (font, glyph, &extents))
+      {
+        *coord = extents.y_bearing + extents.height / 2;
+      }
+      else
+      {
+        hb_position_t x_height = 0;
+        hb_ot_metrics_get_position (font, HB_OT_METRICS_TAG_X_HEIGHT, &x_height);
+        *coord = x_height / 2;
+      }
+    }
+    break;
+
+  case HB_OT_LAYOUT_BASELINE_TAG_IDEO_FACE_TOP_OR_RIGHT:
+  case HB_OT_LAYOUT_BASELINE_TAG_IDEO_FACE_BOTTOM_OR_LEFT:
+    {
+      hb_position_t embox_top, embox_bottom;
+
+      hb_ot_layout_get_baseline_with_fallback (font,
+                                               HB_OT_LAYOUT_BASELINE_TAG_IDEO_EMBOX_TOP_OR_RIGHT,
+                                               direction,
+                                               script_tag,
+                                               language_tag,
+                                               &embox_top);
+      hb_ot_layout_get_baseline_with_fallback (font,
+                                               HB_OT_LAYOUT_BASELINE_TAG_IDEO_EMBOX_BOTTOM_OR_LEFT,
+                                               direction,
+                                               script_tag,
+                                               language_tag,
+                                               &embox_bottom);
+
+      if (baseline_tag == HB_OT_LAYOUT_BASELINE_TAG_IDEO_FACE_TOP_OR_RIGHT)
+        *coord = embox_top + (embox_bottom - embox_top) / 10;
+      else
+        *coord = embox_bottom + (embox_top - embox_bottom) / 10;
+    }
+    break;
+
+  case HB_OT_LAYOUT_BASELINE_TAG_IDEO_EMBOX_TOP_OR_RIGHT:
+    if (hb_ot_layout_get_baseline (font,
+                                   HB_OT_LAYOUT_BASELINE_TAG_IDEO_EMBOX_BOTTOM_OR_LEFT,
+                                   direction,
+                                   script_tag,
+                                   language_tag,
+                                   coord))
+      *coord += HB_DIRECTION_IS_HORIZONTAL (direction) ? font->y_scale : font->x_scale;
+    else
+    {
+      hb_font_extents_t font_extents;
+      hb_font_get_extents_for_direction (font, direction, &font_extents);
+      *coord = font_extents.ascender;
+    }
+    break;
+
+  case HB_OT_LAYOUT_BASELINE_TAG_IDEO_EMBOX_BOTTOM_OR_LEFT:
+    if (hb_ot_layout_get_baseline (font,
+                                   HB_OT_LAYOUT_BASELINE_TAG_IDEO_EMBOX_TOP_OR_RIGHT,
+                                   direction,
+                                   script_tag,
+                                   language_tag,
+                                   coord))
+      *coord -= HB_DIRECTION_IS_HORIZONTAL (direction) ? font->y_scale : font->x_scale;
+    else
+    {
+      hb_font_extents_t font_extents;
+      hb_font_get_extents_for_direction (font, direction, &font_extents);
+      *coord = font_extents.descender;
+    }
+    break;
+
+  case HB_OT_LAYOUT_BASELINE_TAG_HANGING:
+    if (HB_DIRECTION_IS_HORIZONTAL (direction))
+    {
+      hb_codepoint_t ch;
+      hb_codepoint_t glyph;
+      hb_glyph_extents_t extents;
+
+      /* Keep in sync with hb_ot_layout_get_horizontal_baseline_for_script */
+      switch ((int) script_tag)
+      {
+      /* Unicode-1.1 additions */
+      case HB_SCRIPT_BENGALI:          ch = 0x0995u; break;
+      case HB_SCRIPT_DEVANAGARI:       ch = 0x0915u; break;
+      case HB_SCRIPT_GUJARATI:         ch = 0x0a95u; break;
+      case HB_SCRIPT_GURMUKHI:         ch = 0x0a15u; break;
+      /* Unicode-2.0 additions */
+      case HB_SCRIPT_TIBETAN:          ch = 0x0f40u; break;
+      /* Unicode-4.0 additions */
+      case HB_SCRIPT_LIMBU:            ch = 0x1901u; break;
+      /* Unicode-4.1 additions */
+      case HB_SCRIPT_SYLOTI_NAGRI:     ch = 0xa807u; break;
+      /* Unicode-5.0 additions */
+      case HB_SCRIPT_PHAGS_PA:         ch = 0xa840u; break;
+      /* Unicode-5.2 additions */
+      case HB_SCRIPT_MEETEI_MAYEK:     ch = 0xabc0u; break;
+      /* Unicode-6.1 additions */
+      case HB_SCRIPT_SHARADA:          ch = 0x11191u; break;
+      case HB_SCRIPT_TAKRI:            ch = 0x1168cu; break;
+      /* Unicode-7.0 additions */
+      case HB_SCRIPT_MODI:             ch = 0x1160eu;break;
+      case HB_SCRIPT_SIDDHAM:          ch = 0x11590u; break;
+      case HB_SCRIPT_TIRHUTA:          ch = 0x1148fu; break;
+      /* Unicode-9.0 additions */
+      case HB_SCRIPT_MARCHEN:          ch = 0x11c72u; break;
+      case HB_SCRIPT_NEWA:             ch = 0x1140eu; break;
+      /* Unicode-10.0 additions */
+      case HB_SCRIPT_SOYOMBO:          ch = 0x11a5cu; break;
+      case HB_SCRIPT_ZANABAZAR_SQUARE: ch = 0x11a0bu; break;
+      /* Unicode-11.0 additions */
+      case HB_SCRIPT_DOGRA:            ch = 0x1180au; break;
+      case HB_SCRIPT_GUNJALA_GONDI:    ch = 0x11d6cu; break;
+      /* Unicode-12.0 additions */
+      case HB_SCRIPT_NANDINAGARI:      ch = 0x119b0u; break;
+      default:                         ch = 0;        break;
+      }
+
+      if (ch &&
+          hb_font_get_nominal_glyph (font, ch, &glyph) &&
+          hb_font_get_glyph_extents (font, glyph, &extents))
+        *coord = extents.y_bearing;
+      else
+        *coord = font->y_scale * 6 / 10; // FIXME makes assumptions about origin
+    }
+    else
+      *coord = font->x_scale * 6 / 10; // FIXME makes assumptions about origin
+    break;
+
+  case _HB_OT_LAYOUT_BASELINE_TAG_MAX_VALUE:
+  default:
+    *coord = 0;
+    break;
+  }
+}
+
 #endif
 
 
diff --git a/src/hb-ot-layout.h b/src/hb-ot-layout.h
index edbb7b878..22ba7c4ee 100644
--- a/src/hb-ot-layout.h
+++ b/src/hb-ot-layout.h
@@ -522,6 +522,14 @@ hb_ot_layout_get_baseline (hb_font_t                   *font,
 			   hb_tag_t                     language_tag,
 			   hb_position_t               *coord        /* OUT.  May be NULL. */);
 
+HB_EXTERN void
+hb_ot_layout_get_baseline_with_fallback (hb_font_t                   *font,
+					 hb_ot_layout_baseline_tag_t  baseline_tag,
+					 hb_direction_t               direction,
+					 hb_tag_t                     script_tag,
+					 hb_tag_t                     language_tag,
+					 hb_position_t               *coord        /* OUT */);
+
 HB_END_DECLS
 
 #endif /* HB_OT_LAYOUT_H */
diff --git a/test/api/fonts/base2.ttf b/test/api/fonts/base2.ttf
new file mode 100644
index 000000000..5cb0d35ba
Binary files /dev/null and b/test/api/fonts/base2.ttf differ
diff --git a/test/api/test-baseline.c b/test/api/test-baseline.c
index 982c68311..9f9542ea4 100644
--- a/test/api/test-baseline.c
+++ b/test/api/test-baseline.c
@@ -41,6 +41,58 @@ test_ot_layout_base (void)
 				       &position));
   g_assert_cmpint (46, ==, position);
 
+  g_assert (!hb_ot_layout_get_baseline (font, HB_OT_LAYOUT_BASELINE_TAG_IDEO_EMBOX_TOP_OR_RIGHT, HB_DIRECTION_TTB,
+				        HB_TAG ('h','a','n','i'),
+				        HB_TAG ('E','N','G',' '),
+				        &position));
+
+  hb_font_destroy (font);
+  hb_face_destroy (face);
+}
+
+static void
+test_ot_layout_base_with_fallback (void)
+{
+  hb_face_t *face = hb_test_open_font_file ("fonts/base.ttf");
+  hb_font_t *font = hb_font_create (face);
+
+  hb_position_t position;
+  hb_ot_layout_get_baseline_with_fallback (font, HB_OT_LAYOUT_BASELINE_TAG_IDEO_FACE_BOTTOM_OR_LEFT, HB_DIRECTION_TTB,
+					   HB_TAG ('h','a','n','i'),
+					   HB_TAG ('E','N','G',' '),
+					   &position);
+  g_assert_cmpint (46, ==, position);
+
+  hb_ot_layout_get_baseline_with_fallback (font, HB_OT_LAYOUT_BASELINE_TAG_IDEO_EMBOX_TOP_OR_RIGHT, HB_DIRECTION_TTB,
+					   HB_TAG ('h','a','n','i'),
+					   HB_TAG ('E','N','G',' '),
+					   &position);
+  g_assert_cmpint (1000, ==, position);
+
+  hb_ot_layout_get_baseline_with_fallback (font, HB_OT_LAYOUT_BASELINE_TAG_MATH, HB_DIRECTION_LTR,
+					   HB_TAG ('h','a','n','i'),
+					   HB_TAG ('E','N','G',' '),
+					   &position);
+  g_assert_cmpint (271, ==, position);
+
+  hb_font_destroy (font);
+  hb_face_destroy (face);
+
+  face = hb_test_open_font_file ("fonts/base2.ttf");
+  font = hb_font_create (face);
+
+  hb_ot_layout_get_baseline_with_fallback (font, HB_OT_LAYOUT_BASELINE_TAG_HANGING, HB_DIRECTION_LTR,
+					   HB_SCRIPT_BENGALI,
+					   HB_TAG ('E','N','G',' '),
+					   &position);
+  g_assert_cmpint (622, ==, position);
+
+  hb_ot_layout_get_baseline_with_fallback (font, HB_OT_LAYOUT_BASELINE_TAG_HANGING, HB_DIRECTION_LTR,
+					   HB_SCRIPT_TIBETAN,
+					   HB_TAG ('E','N','G',' '),
+					   &position);
+  g_assert_cmpint (600, ==, position);
+
   hb_font_destroy (font);
   hb_face_destroy (face);
 }
@@ -51,6 +103,7 @@ main (int argc, char **argv)
   hb_test_init (&argc, &argv);
 
   hb_test_add (test_ot_layout_base);
+  hb_test_add (test_ot_layout_base_with_fallback);
 
   return hb_test_run();
 }