diff --git a/docs/versionhistory.rst b/docs/versionhistory.rst
index 902d875..af93517 100644
--- a/docs/versionhistory.rst
+++ b/docs/versionhistory.rst
@@ -6,6 +6,8 @@ This library adheres to
 
 **UNRELEASED**
 
+- Fixed some compatibility problems when running on Python 3.13
+  (`#460 <https://github.com/agronholm/typeguard/issues/460>`_)
 - Fixed test suite incompatibility with pytest 8.2
   (`#461 <https://github.com/agronholm/typeguard/issues/461>`_)
 
diff --git a/pyproject.toml b/pyproject.toml
index 495312c..d427b58 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -26,7 +26,7 @@ classifiers = [
 requires-python = ">= 3.8"
 dependencies = [
     "importlib_metadata >= 3.6; python_version < '3.10'",
-    "typing_extensions >= 4.10.0; python_version < '3.13'",
+    "typing_extensions >= 4.10.0",
 ]
 dynamic = ["version"]
 
diff --git a/src/typeguard/_checkers.py b/src/typeguard/_checkers.py
index 2f8de6f..0203f4e 100644
--- a/src/typeguard/_checkers.py
+++ b/src/typeguard/_checkers.py
@@ -38,16 +38,17 @@
 except ImportError:
     typing_extensions = None  # type: ignore[assignment]
 
+# Must use this because typing.is_typeddict does not recognize
+# TypedDict from typing_extensions, and as of version 4.12.0
+# typing_extensions.TypedDict is different from typing.TypedDict
+# on all versions.
+from typing_extensions import is_typeddict
+
 from ._config import ForwardRefPolicy
 from ._exceptions import TypeCheckError, TypeHintWarning
 from ._memo import TypeCheckMemo
 from ._utils import evaluate_forwardref, get_stacklevel, get_type_name, qualified_name
 
-if sys.version_info >= (3, 13):
-    from typing import is_typeddict
-else:
-    from typing_extensions import is_typeddict
-
 if sys.version_info >= (3, 11):
     from typing import (
         Annotated,
diff --git a/src/typeguard/_utils.py b/src/typeguard/_utils.py
index 96818fd..9bcc841 100644
--- a/src/typeguard/_utils.py
+++ b/src/typeguard/_utils.py
@@ -11,11 +11,21 @@
 if TYPE_CHECKING:
     from ._memo import TypeCheckMemo
 
-if sys.version_info >= (3, 10):
+if sys.version_info >= (3, 13):
     from typing import get_args, get_origin
 
     def evaluate_forwardref(forwardref: ForwardRef, memo: TypeCheckMemo) -> Any:
-        return forwardref._evaluate(memo.globals, memo.locals, frozenset())
+        return forwardref._evaluate(
+            memo.globals, memo.locals, type_params=(), recursive_guard=frozenset()
+        )
+
+elif sys.version_info >= (3, 10):
+    from typing import get_args, get_origin
+
+    def evaluate_forwardref(forwardref: ForwardRef, memo: TypeCheckMemo) -> Any:
+        return forwardref._evaluate(
+            memo.globals, memo.locals, recursive_guard=frozenset()
+        )
 
 else:
     from typing_extensions import get_args, get_origin
diff --git a/tests/test_checkers.py b/tests/test_checkers.py
index 29b1b01..c3233d8 100644
--- a/tests/test_checkers.py
+++ b/tests/test_checkers.py
@@ -43,6 +43,7 @@
     check_type_internal,
     suppress_type_checks,
 )
+from typeguard._checkers import is_typeddict
 from typeguard._utils import qualified_name
 
 from . import (
@@ -530,6 +531,14 @@ class DummyDict(typing_provider.TypedDict):
         ):
             check_type({"x": 1, "y": "foo"}, DummyDict)
 
+    def test_is_typeddict(self, typing_provider):
+        # Ensure both typing.TypedDict and typing_extensions.TypedDict are recognized
+        class DummyDict(typing_provider.TypedDict):
+            x: int
+
+        assert is_typeddict(DummyDict)
+        assert not is_typeddict(dict)
+
 
 class TestList:
     def test_bad_type(self):