diff --git a/pandas-stubs/core/indexes/base.pyi b/pandas-stubs/core/indexes/base.pyi
index 2cef882ec..9fb20aff8 100644
--- a/pandas-stubs/core/indexes/base.pyi
+++ b/pandas-stubs/core/indexes/base.pyi
@@ -403,8 +403,8 @@ class Index(IndexOpsMixin[S1]):
     def slice_indexer(self, start=..., end=..., step=...): ...
     def get_slice_bound(self, label, side): ...
     def slice_locs(self, start=..., end=..., step=...): ...
-    def delete(self, loc): ...
-    def insert(self, loc, item): ...
+    def delete(self, loc) -> Self: ...
+    def insert(self, loc, item) -> Self: ...
     def drop(self, labels, errors: _str = ...) -> Self: ...
     @property
     def shape(self) -> tuple[int, ...]: ...
diff --git a/pandas-stubs/core/indexes/datetimes.pyi b/pandas-stubs/core/indexes/datetimes.pyi
index c1f596c48..7ed87864c 100644
--- a/pandas-stubs/core/indexes/datetimes.pyi
+++ b/pandas-stubs/core/indexes/datetimes.pyi
@@ -80,7 +80,6 @@ class DatetimeIndex(DatetimeTimedeltaMixin[Timestamp], DatetimeIndexProperties):
     def searchsorted(self, value, side: str = ..., sorter=...): ...
     @property
     def inferred_type(self) -> str: ...
-    def insert(self, loc, item): ...
     def indexer_at_time(self, time, asof: bool = ...): ...
     def indexer_between_time(
         self, start_time, end_time, include_start: bool = ..., include_end: bool = ...
diff --git a/pandas-stubs/core/indexes/timedeltas.pyi b/pandas-stubs/core/indexes/timedeltas.pyi
index 59b2c7aa3..4b486e855 100644
--- a/pandas-stubs/core/indexes/timedeltas.pyi
+++ b/pandas-stubs/core/indexes/timedeltas.pyi
@@ -75,7 +75,6 @@ class TimedeltaIndex(DatetimeTimedeltaMixin[Timedelta], TimedeltaIndexProperties
     def searchsorted(self, value, side: str = ..., sorter=...): ...
     @property
     def inferred_type(self) -> str: ...
-    def insert(self, loc, item): ...
     def to_series(self, index=..., name: Hashable = ...) -> TimedeltaSeries: ...
     def shift(self, periods: int = ..., freq=...) -> Self: ...
 
diff --git a/tests/test_indexes.py b/tests/test_indexes.py
index f276fdba1..1c91add0b 100644
--- a/tests/test_indexes.py
+++ b/tests/test_indexes.py
@@ -1287,3 +1287,33 @@ def test_datetimeindex_shift() -> None:
 def test_timedeltaindex_shift() -> None:
     ind = pd.date_range("1/1/2021", "1/5/2021") - pd.Timestamp("1/3/2019")
     check(assert_type(ind.shift(1), pd.TimedeltaIndex), pd.TimedeltaIndex)
+
+
+def test_index_insert() -> None:
+    """Test the return type of Index.insert GH1196."""
+    idx = pd.Index([1, 2, 3, 4, 5])
+    check(assert_type(idx.insert(2, 3), "pd.Index[int]"), pd.Index, np.integer)
+
+    ind = pd.date_range("1/1/2021", "1/5/2021") - pd.Timestamp("1/3/2019")
+    check(
+        assert_type(ind.insert(2, pd.Timedelta("1D")), pd.TimedeltaIndex),
+        pd.TimedeltaIndex,
+    )
+
+    dt_ind = pd.date_range("2023-01-01", "2023-02-01")
+    check(
+        assert_type(dt_ind.insert(2, pd.Timestamp(2024, 3, 5)), pd.DatetimeIndex),
+        pd.DatetimeIndex,
+    )
+
+
+def test_index_delete() -> None:
+    """Test the return type of Index.delete GH1196."""
+    idx = pd.Index([1, 2, 3, 4, 5])
+    check(assert_type(idx.delete(2), "pd.Index[int]"), pd.Index, np.integer)
+
+    ind = pd.date_range("1/1/2021", "1/5/2021") - pd.Timestamp("1/3/2019")
+    check(assert_type(ind.delete(2), pd.TimedeltaIndex), pd.TimedeltaIndex)
+
+    dt_ind = pd.date_range("2023-01-01", "2023-02-01")
+    check(assert_type(dt_ind.delete(2), pd.DatetimeIndex), pd.DatetimeIndex)