diff --git a/tests/test_typing.py b/tests/test_typing.py
index 592955d7..a5c7c7b1 100644
--- a/tests/test_typing.py
+++ b/tests/test_typing.py
@@ -249,7 +249,7 @@ class T(HasTraits):
 @pytest.mark.mypy_testing
 def mypy_set_typing() -> None:
     class T(HasTraits):
-        remove_cell_tags = Set(
+        remove_cell_tags: Set[t.Any] = Set(
             Unicode(),
             default_value=[],
             help=(
@@ -258,7 +258,7 @@ class T(HasTraits):
             ),
         ).tag(config=True)
 
-        safe_output_keys = Set(
+        safe_output_keys: Set[str] = Set(
             config=True,
             default_value={
                 "metadata",  # Not a mimetype per-se, but expected and safe.
@@ -272,14 +272,14 @@ class T(HasTraits):
         )
 
     t = T()
-    reveal_type(Set("foo"))  # R: traitlets.traitlets.Set
-    reveal_type(Set("").tag(sync=True))  # R: traitlets.traitlets.Set
-    reveal_type(Set(None, allow_none=True))  # R: traitlets.traitlets.Set
-    reveal_type(Set(None, allow_none=True).tag(sync=True))  # R: traitlets.traitlets.Set
-    reveal_type(T.remove_cell_tags)  # R: traitlets.traitlets.Set
+    reveal_type(Set("foo"))  # R: traitlets.traitlets.Set[Never]
+    reveal_type(Set("").tag(sync=True))  # R: traitlets.traitlets.Set[Never]
+    reveal_type(Set(None, allow_none=True))  # R: traitlets.traitlets.Set[Never]
+    reveal_type(Set(None, allow_none=True).tag(sync=True))  # R: traitlets.traitlets.Set[Never]
+    reveal_type(T.remove_cell_tags)  # R: traitlets.traitlets.Set[Any]
     reveal_type(t.remove_cell_tags)  # R: set[Any]
-    reveal_type(T.safe_output_keys)  # R: traitlets.traitlets.Set
-    reveal_type(t.safe_output_keys)  # R: set[Any]
+    reveal_type(T.safe_output_keys)  # R: traitlets.traitlets.Set[str]
+    reveal_type(t.safe_output_keys)  # R: set[str]
 
 
 @pytest.mark.mypy_testing
@@ -452,3 +452,13 @@ class T(HasTraits):
     t.inst = "foo"  # E: Incompatible types in assignment (expression has type "str", variable has type "Foo")  [assignment]
     t.oinst = "foo"  # E: Incompatible types in assignment (expression has type "str", variable has type "Foo | None")  [assignment]
     t.inst = None  # E: Incompatible types in assignment (expression has type "None", variable has type "Foo")  [assignment]
+
+
+@pytest.mark.mypy_testing
+def mypy_generic_set_typing() -> None:
+    class T(HasTraits):
+        values: Set[str] = Set()
+
+    t = T()
+    reveal_type(T.values)  # R: traitlets.traitlets.Set[str]
+    reveal_type(t.values)  # R: set[str]
diff --git a/traitlets/traitlets.py b/traitlets/traitlets.py
index 2cc239c1..2bfbd922 100644
--- a/traitlets/traitlets.py
+++ b/traitlets/traitlets.py
@@ -3676,10 +3676,10 @@ def set(self, obj: t.Any, value: t.Any) -> None:
             return super().set(obj, value)
 
 
-class Set(Container[set[t.Any]]):
+class Set(Container[set[T]]):
     """An instance of a Python set."""
 
-    klass = set
+    klass = set  # type: ignore[assignment]
     _cast_types = (tuple, list)
 
     _literal_from_string_pairs = ("[]", "()", "{}")
@@ -3739,13 +3739,14 @@ def validate_elements(self, obj: t.Any, value: t.Any) -> t.Any:
 
     def set(self, obj: t.Any, value: t.Any) -> None:
         if isinstance(value, str):
-            return super().set(obj, {value})
+            return super().set(obj, {t.cast(T, value)})
         else:
             return super().set(obj, value)
 
     def default_value_repr(self) -> str:
         # Ensure default value is sorted for a reproducible build
-        list_repr = repr(sorted(self.make_dynamic_default() or []))
+        default = t.cast(set[t.Any] | None, self.make_dynamic_default()) or set()
+        list_repr = repr(sorted(default))
         if list_repr == "[]":
             return "set()"
         return "{" + list_repr[1:-1] + "}"