diff --git a/pdoc/__init__.py b/pdoc/__init__.py
index 8d8c3b09..90fc0d5b 100644
--- a/pdoc/__init__.py
+++ b/pdoc/__init__.py
@@ -1403,6 +1403,19 @@ def maybe_replace_reprs(a):
     return str(inspect.formatannotation(maybe_replace_reprs(annot)))
 
 
+class _PermissiveFallback:
+    """
+    Returns `Any` for missing attributes (used for annotation-only
+    modules where the installed version is missingm newer names, e.g.
+    `typing_extensions.CapsuleType` on Python < 3.13).
+    """
+    def __init__(self, mod):
+        self._mod = mod
+
+    def __getattr__(self, name):
+        return getattr(self._mod, name, Any)
+
+
 class Function(Doc):
     """
     Representation of documentation for a function or method.
@@ -1648,9 +1661,30 @@ def _signature_from_string(self):
             if strings:
                 string = filter(strings[0])
                 _locals, _globals = {}, {}
-                _globals.update({'capsule': None})  # pybind11 capsule data type
+                _globals.update({'capsule': Any})  # pybind11 capsule data type
+
+                # pybind11 >= 3.0.0 uses typing.SupportsInt, etc.
+                _globals['typing'] = typing
                 _globals.update(typing.__dict__)
+
+                # types is optional and may lack newer names
+                # (e.g. types.CapsuleType) depending on installed version
+                try:
+                    import types
+                    _globals['types'] = _PermissiveFallback(types)
+                except ImportError:
+                    pass
+
+                # typing_extensions is optional and may lack newer names
+                # (e.g. typing_extensions.CapsuleType) depending on installed version
+                try:
+                    import typing_extensions
+                    _globals['typing_extensions'] = _PermissiveFallback(typing_extensions)
+                except ImportError:
+                    pass
+
                 _globals.update(self.module.obj.__dict__)
+
                 # Trim binding module basename from type annotations
                 # See: https://github.com/pdoc3/pdoc/pull/148#discussion_r407114141
                 module_basename = self.module.name.rsplit('.', maxsplit=1)[-1]
diff --git a/pdoc/test/__init__.py b/pdoc/test/__init__.py
index bc4a3a6f..cec6c0f7 100644
--- a/pdoc/test/__init__.py
+++ b/pdoc/test/__init__.py
@@ -3,6 +3,7 @@
 """
 import doctest
 import enum
+import importlib.util
 import inspect
 import os
 import shutil
@@ -104,6 +105,13 @@ def wrapper(*args, **kwargs):
     return wrapper
 
 
+def has_typing_extensions_capsule_type():
+    if importlib.util.find_spec('typing_extensions') is None:
+        return False
+    import typing_extensions
+    return hasattr(typing_extensions, 'CapsuleType')
+
+
 class CliTest(unittest.TestCase):
     """
     Command-line interface unit tests.
@@ -1018,6 +1026,94 @@ def f() -> typing.List[typing.Union[str, pdoc.Doc]]: return []  # noqa: E704
         func = pdoc.Function('f', DUMMY_PDOC_MODULE, f)
         self.assertEqual(func.return_annotation(), 'List[str\N{NBSP}|\N{NBSP}pdoc.Doc]')
 
+    def test_Function_signature_from_string(self):
+        fake_module = ModuleType('fake_pybind11_module')
+        # sanity check the isolation itself
+        assert 'typing' not in fake_module.__dict__
+        mod = pdoc.Module(fake_module)
+
+        # Union types with `|` operator where introduces with Python 3.10
+        if sys.version_info >= (3, 10):
+            class pybind11_int:
+                """
+                pybind11_int(self: str, pos: typing.SupportsInt | typing.SupportsIndex) -> \
+                    tuple[int, float]
+                """
+            func = pdoc.Function('pybind11_int', mod, pybind11_int)
+            sig = pdoc.Function._signature_from_string(func)
+
+            def expected_pybind11_int(
+                    self: str, pos: typing.SupportsInt | typing.SupportsIndex) \
+                    -> tuple[int, float]:
+                raise NotImplementedError
+            self.assertEqual(sig, inspect.signature(expected_pybind11_int))
+
+            class pybind11_float:
+                """
+                pybind11_float(self: str, pos: typing.SupportsFloat | typing.SupportsIndex) -> \
+                    tuple[int, float]
+                """
+            func = pdoc.Function('pybind11_float', mod, pybind11_float)
+            sig = pdoc.Function._signature_from_string(func)
+
+            def expected_pybind11_float(
+                    self: str, pos: typing.SupportsFloat | typing.SupportsIndex) \
+                    -> tuple[int, float]:
+                raise NotImplementedError
+            self.assertEqual(sig, inspect.signature(expected_pybind11_float))
+        else:
+            class pybind11_int:
+                """
+                pybind11_int(self: str, pos: typing.SupportsInt) -> tuple[int, float]
+                """
+            func = pdoc.Function('pybind11_int', mod, pybind11_int)
+            sig = pdoc.Function._signature_from_string(func)
+
+            def expected_pybind11_int(self: str, pos: typing.SupportsInt) -> tuple[int, float]:
+                raise NotImplementedError
+            self.assertEqual(sig, inspect.signature(expected_pybind11_int))
+
+            class pybind11_float:
+                """
+                pybind11_float(self: str, pos: typing.SupportsFloat) -> tuple[int, float]
+                """
+            func = pdoc.Function('pybind11_float', mod, pybind11_float)
+            sig = pdoc.Function._signature_from_string(func)
+
+            def expected_pybind11_float(self: str, pos: typing.SupportsFloat) -> tuple[int, float]:
+                raise NotImplementedError
+            self.assertEqual(sig, inspect.signature(expected_pybind11_float))
+
+        if sys.version_info >= (3, 13):
+            import types
+
+            class pybind11_capsule:
+                """
+                pybind11_capsule(self: str, pointer: types.CapsuleType) -> tuple[int, float]
+                """
+            func = pdoc.Function('pybind11_capsule', mod, pybind11_capsule)
+            sig = pdoc.Function._signature_from_string(func)
+
+            def expected_pybind11_capsule(
+                    self: str, pointer: types.CapsuleType) -> tuple[int, float]:
+                raise NotImplementedError
+            self.assertEqual(sig, inspect.signature(expected_pybind11_capsule))
+        elif has_typing_extensions_capsule_type():
+            import typing_extensions
+
+            class pybind11_capsule:
+                """
+                pybind11_capsule(self: str, pointer: typing_extensions.CapsuleType) -> \
+                    tuple[int, float]
+                """
+            func = pdoc.Function('pybind11_capsule', mod, pybind11_capsule)
+            sig = pdoc.Function._signature_from_string(func)
+
+            def expected_pybind11_capsule(
+                    self: str, pointer: typing_extensions.CapsuleType) -> tuple[int, float]:
+                raise NotImplementedError
+            self.assertEqual(sig, inspect.signature(expected_pybind11_capsule))
+
     @ignore_warnings
     def test_Variable_type_annotation(self):
         class Foobar: