diff --git a/pandas/core/internals/base.py b/pandas/core/internals/base.py
index 0fd91b163aba9..b03b98d89ccd5 100644
--- a/pandas/core/internals/base.py
+++ b/pandas/core/internals/base.py
@@ -284,7 +284,11 @@ def replace_list(
 
     def interpolate(self, inplace: bool, **kwargs) -> Self:
         return self.apply_with_block(
-            "interpolate", inplace=inplace, **kwargs, using_cow=using_copy_on_write()
+            "interpolate",
+            inplace=inplace,
+            **kwargs,
+            using_cow=using_copy_on_write(),
+            already_warned=_AlreadyWarned(),
         )
 
     def pad_or_backfill(self, inplace: bool, **kwargs) -> Self:
@@ -293,6 +297,7 @@ def pad_or_backfill(self, inplace: bool, **kwargs) -> Self:
             inplace=inplace,
             **kwargs,
             using_cow=using_copy_on_write(),
+            already_warned=_AlreadyWarned(),
         )
 
     def shift(self, periods: int, fill_value) -> Self:
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 85780bad1e403..f0f8430c991ad 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -1657,6 +1657,7 @@ def pad_or_backfill(
         limit_area: Literal["inside", "outside"] | None = None,
         downcast: Literal["infer"] | None = None,
         using_cow: bool = False,
+        already_warned=None,
     ) -> list[Block]:
         if not self._can_hold_na:
             # If there are no NAs, then interpolate is a no-op
@@ -1677,6 +1678,19 @@ def pad_or_backfill(
             limit_area=limit_area,
             copy=copy,
         )
+        if (
+            not copy
+            and warn_copy_on_write()
+            and already_warned is not None
+            and not already_warned.warned_already
+        ):
+            if self.refs.has_reference():
+                warnings.warn(
+                    COW_WARNING_GENERAL_MSG,
+                    FutureWarning,
+                    stacklevel=find_stack_level(),
+                )
+                already_warned.warned_already = True
         if axis == 1:
             new_values = new_values.T
 
@@ -1697,6 +1711,7 @@ def interpolate(
         limit_area: Literal["inside", "outside"] | None = None,
         downcast: Literal["infer"] | None = None,
         using_cow: bool = False,
+        already_warned=None,
         **kwargs,
     ) -> list[Block]:
         inplace = validate_bool_kwarg(inplace, "inplace")
@@ -1735,6 +1750,20 @@ def interpolate(
         )
         data = extract_array(new_values, extract_numpy=True)
 
+        if (
+            not copy
+            and warn_copy_on_write()
+            and already_warned is not None
+            and not already_warned.warned_already
+        ):
+            if self.refs.has_reference():
+                warnings.warn(
+                    COW_WARNING_GENERAL_MSG,
+                    FutureWarning,
+                    stacklevel=find_stack_level(),
+                )
+                already_warned.warned_already = True
+
         nb = self.make_block_same_class(data, refs=refs)
         return nb._maybe_downcast([nb], downcast, using_cow, caller="interpolate")
 
@@ -2178,9 +2207,9 @@ def pad_or_backfill(
         limit_area: Literal["inside", "outside"] | None = None,
         downcast: Literal["infer"] | None = None,
         using_cow: bool = False,
+        already_warned=None,
     ) -> list[Block]:
         values = self.values
-        copy, refs = self._get_refs_and_copy(using_cow, inplace)
 
         if values.ndim == 2 and axis == 1:
             # NDArrayBackedExtensionArray.fillna assumes axis=0
diff --git a/pandas/tests/copy_view/test_chained_assignment_deprecation.py b/pandas/tests/copy_view/test_chained_assignment_deprecation.py
index b51a5920917d6..2829617c84cd2 100644
--- a/pandas/tests/copy_view/test_chained_assignment_deprecation.py
+++ b/pandas/tests/copy_view/test_chained_assignment_deprecation.py
@@ -42,11 +42,16 @@ def test_methods_iloc_warn(using_copy_on_write):
         ("ffill", ()),
     ],
 )
-def test_methods_iloc_getitem_item_cache(func, args, using_copy_on_write):
-    df = DataFrame({"a": [1, 2, 3], "b": 1})
+def test_methods_iloc_getitem_item_cache(
+    func, args, using_copy_on_write, warn_copy_on_write
+):
+    df = DataFrame({"a": [1.5, 2, 3], "b": 1.5})
     ser = df.iloc[:, 0]
-    # TODO(CoW-warn) should warn about updating a view
-    getattr(ser, func)(*args, inplace=True)
+    # TODO(CoW-warn) should warn about updating a view for all methods
+    with tm.assert_cow_warning(
+        warn_copy_on_write and func not in ("replace", "fillna")
+    ):
+        getattr(ser, func)(*args, inplace=True)
 
     # parent that holds item_cache is dead, so don't increase ref count
     ser = df.copy()["a"]
diff --git a/pandas/tests/copy_view/test_interp_fillna.py b/pandas/tests/copy_view/test_interp_fillna.py
index 7849799eb2cc4..ddc5879a56d54 100644
--- a/pandas/tests/copy_view/test_interp_fillna.py
+++ b/pandas/tests/copy_view/test_interp_fillna.py
@@ -91,12 +91,13 @@ def test_interpolate_inplace_no_reference_no_copy(using_copy_on_write, vals):
 @pytest.mark.parametrize(
     "vals", [[1, np.nan, 2], [Timestamp("2019-12-31"), NaT, Timestamp("2020-12-31")]]
 )
-def test_interpolate_inplace_with_refs(using_copy_on_write, vals):
+def test_interpolate_inplace_with_refs(using_copy_on_write, vals, warn_copy_on_write):
     df = DataFrame({"a": [1, np.nan, 2]})
     df_orig = df.copy()
     arr = get_array(df, "a")
     view = df[:]
-    df.interpolate(method="linear", inplace=True)
+    with tm.assert_cow_warning(warn_copy_on_write):
+        df.interpolate(method="linear", inplace=True)
 
     if using_copy_on_write:
         # Check that copy was triggered in interpolate and that we don't
@@ -109,6 +110,31 @@ def test_interpolate_inplace_with_refs(using_copy_on_write, vals):
         assert np.shares_memory(arr, get_array(df, "a"))
 
 
+@pytest.mark.parametrize("func", ["ffill", "bfill"])
+@pytest.mark.parametrize("dtype", ["float64", "Float64"])
+def test_interp_fill_functions_inplace(
+    using_copy_on_write, func, warn_copy_on_write, dtype
+):
+    # Check that these takes the same code paths as interpolate
+    df = DataFrame({"a": [1, np.nan, 2]}, dtype=dtype)
+    df_orig = df.copy()
+    arr = get_array(df, "a")
+    view = df[:]
+
+    with tm.assert_cow_warning(warn_copy_on_write and dtype == "float64"):
+        getattr(df, func)(inplace=True)
+
+    if using_copy_on_write:
+        # Check that copy was triggered in interpolate and that we don't
+        # have any references left
+        assert not np.shares_memory(arr, get_array(df, "a"))
+        tm.assert_frame_equal(df_orig, view)
+        assert df._mgr._has_no_reference(0)
+        assert view._mgr._has_no_reference(0)
+    else:
+        assert np.shares_memory(arr, get_array(df, "a")) is (dtype == "float64")
+
+
 def test_interpolate_cleaned_fill_method(using_copy_on_write):
     # Check that "method is set to None" case works correctly
     df = DataFrame({"a": ["a", np.nan, "c"], "b": 1})
diff --git a/pandas/tests/copy_view/test_methods.py b/pandas/tests/copy_view/test_methods.py
index 558b483933f25..862aebdc70a9d 100644
--- a/pandas/tests/copy_view/test_methods.py
+++ b/pandas/tests/copy_view/test_methods.py
@@ -1607,7 +1607,8 @@ def test_interpolate_creates_copy(using_copy_on_write, warn_copy_on_write):
     view = df[:]
     expected = df.copy()
 
-    df.ffill(inplace=True)
+    with tm.assert_cow_warning(warn_copy_on_write):
+        df.ffill(inplace=True)
     with tm.assert_cow_warning(warn_copy_on_write):
         df.iloc[0, 0] = 100.5