diff --git a/lib/matplotlib/tests/test_backends_interactive.py b/lib/matplotlib/tests/test_backends_interactive.py
index d624b5db0ac2..2c6b61a48438 100644
--- a/lib/matplotlib/tests/test_backends_interactive.py
+++ b/lib/matplotlib/tests/test_backends_interactive.py
@@ -81,10 +81,18 @@ def _get_available_interactive_backends():
         elif env["MPLBACKEND"] == 'macosx' and os.environ.get('TF_BUILD'):
             reason = "macosx backend fails on Azure"
         elif env["MPLBACKEND"].startswith('gtk'):
-            import gi  # type: ignore
+            try:
+                import gi  # type: ignore
+            except ImportError:
+                # Though we check that `gi` exists above, it is possible that its
+                # C-level dependencies are not available, and then it still raises an
+                # `ImportError`, so guard against that.
+                available_gtk_versions = []
+            else:
+                gi_repo = gi.Repository.get_default()
+                available_gtk_versions = gi_repo.enumerate_versions('Gtk')
             version = env["MPLBACKEND"][3]
-            repo = gi.Repository.get_default()
-            if f'{version}.0' not in repo.enumerate_versions('Gtk'):
+            if f'{version}.0' not in available_gtk_versions:
                 reason = "no usable GTK bindings"
         marks = []
         if reason:
diff --git a/pyproject.toml b/pyproject.toml
index 52bbe308c0f9..891ef87e4342 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -49,7 +49,7 @@ requires-python = ">=3.9"
 dev = [
     "meson-python>=0.13.1",
     "numpy>=1.25",
-    "pybind11>=2.6",
+    "pybind11>=2.6,!=2.13.3",
     "setuptools_scm>=7",
     # Not required by us but setuptools_scm without a version, cso _if_
     # installed, then setuptools_scm 8 requires at least this version.
@@ -73,7 +73,7 @@ build-backend = "mesonpy"
 # Also keep in sync with optional dependencies above.
 requires = [
     "meson-python>=0.13.1",
-    "pybind11>=2.6",
+    "pybind11>=2.6,!=2.13.3",
     "setuptools_scm>=7",
 
     # Comments on numpy build requirement range: