diff --git a/Lib/inspect.py b/Lib/inspect.py
index 531b891..6d43d8d 100644
--- a/Lib/inspect.py
+++ b/Lib/inspect.py
@@ -859,7 +859,7 @@ def getmodule(object, _filename=None):
     # Try the cache again with the absolute file name
     try:
         file = getabsfile(object, _filename)
-    except TypeError:
+    except (TypeError, FileNotFoundError):
         return None
     if file in modulesbyfile:
         return sys.modules.get(modulesbyfile[file])
diff --git a/Lib/test/test_inspect.py b/Lib/test/test_inspect.py
index 4164634..93ff2f8 100644
--- a/Lib/test/test_inspect.py
+++ b/Lib/test/test_inspect.py
@@ -493,6 +493,15 @@ def test_getmodule(self):
         # Check filename override
         self.assertEqual(inspect.getmodule(None, modfile), mod)
 
+    def test_getmodule_file_not_found(self):
+        # See bpo-45406
+        def _getabsfile(obj, _filename):
+            raise FileNotFoundError('bad file')
+        with unittest.mock.patch('inspect.getabsfile', _getabsfile):
+            f = inspect.currentframe()
+            self.assertIsNone(inspect.getmodule(f))
+            inspect.getouterframes(f)  # smoke test
+
     def test_getframeinfo_get_first_line(self):
         frame_info = inspect.getframeinfo(self.fodderModule.fr, 50)
         self.assertEqual(frame_info.code_context[0], "# line 1\n")