diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index fed92dc80a99b..83d14571b06e3 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -10916,7 +10916,7 @@ def to_timestamp(
         freq: Frequency | None = None,
         how: str = "start",
         axis: Axis = 0,
-        copy: bool = True,
+        copy: bool | None = None,
     ) -> DataFrame:
         """
         Cast to DatetimeIndex of timestamps, at *beginning* of period.
@@ -10951,7 +10951,7 @@ def to_timestamp(
         return new_obj
 
     def to_period(
-        self, freq: Frequency | None = None, axis: Axis = 0, copy: bool = True
+        self, freq: Frequency | None = None, axis: Axis = 0, copy: bool | None = None
     ) -> DataFrame:
         """
         Convert DataFrame from DatetimeIndex to PeriodIndex.
diff --git a/pandas/core/series.py b/pandas/core/series.py
index b5d73373f061e..612e36c04c23a 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -5623,7 +5623,7 @@ def to_timestamp(
         self,
         freq=None,
         how: Literal["s", "e", "start", "end"] = "start",
-        copy: bool = True,
+        copy: bool | None = None,
     ) -> Series:
         """
         Cast to DatetimeIndex of Timestamps, at *beginning* of period.
@@ -5642,18 +5642,15 @@ def to_timestamp(
         -------
         Series with DatetimeIndex
         """
-        new_values = self._values
-        if copy:
-            new_values = new_values.copy()
-
         if not isinstance(self.index, PeriodIndex):
             raise TypeError(f"unsupported Type {type(self.index).__name__}")
+
+        new_obj = self.copy(deep=copy)
         new_index = self.index.to_timestamp(freq=freq, how=how)
-        return self._constructor(new_values, index=new_index).__finalize__(
-            self, method="to_timestamp"
-        )
+        setattr(new_obj, "index", new_index)
+        return new_obj
 
-    def to_period(self, freq: str | None = None, copy: bool = True) -> Series:
+    def to_period(self, freq: str | None = None, copy: bool | None = None) -> Series:
         """
         Convert Series from DatetimeIndex to PeriodIndex.
 
@@ -5669,16 +5666,13 @@ def to_period(self, freq: str | None = None, copy: bool = True) -> Series:
         Series
             Series with index converted to PeriodIndex.
         """
-        new_values = self._values
-        if copy:
-            new_values = new_values.copy()
-
         if not isinstance(self.index, DatetimeIndex):
             raise TypeError(f"unsupported Type {type(self.index).__name__}")
+
+        new_obj = self.copy(deep=copy)
         new_index = self.index.to_period(freq=freq)
-        return self._constructor(new_values, index=new_index).__finalize__(
-            self, method="to_period"
-        )
+        setattr(new_obj, "index", new_index)
+        return new_obj
 
     @overload
     def ffill(
diff --git a/pandas/tests/copy_view/test_methods.py b/pandas/tests/copy_view/test_methods.py
index 933eea029a205..b41490f245d71 100644
--- a/pandas/tests/copy_view/test_methods.py
+++ b/pandas/tests/copy_view/test_methods.py
@@ -5,7 +5,9 @@
     DataFrame,
     Index,
     MultiIndex,
+    Period,
     Series,
+    Timestamp,
     date_range,
 )
 import pandas._testing as tm
@@ -306,6 +308,42 @@ def test_chained_methods(request, method, idx, using_copy_on_write):
         tm.assert_frame_equal(df2.iloc[:, idx:], df_orig)
 
 
+@pytest.mark.parametrize("obj", [Series([1, 2], name="a"), DataFrame({"a": [1, 2]})])
+def test_to_timestamp(using_copy_on_write, obj):
+    obj.index = Index([Period("2012-1-1", freq="D"), Period("2012-1-2", freq="D")])
+
+    obj_orig = obj.copy()
+    obj2 = obj.to_timestamp()
+
+    if using_copy_on_write:
+        assert np.shares_memory(get_array(obj2, "a"), get_array(obj, "a"))
+    else:
+        assert not np.shares_memory(get_array(obj2, "a"), get_array(obj, "a"))
+
+    # mutating obj2 triggers a copy-on-write for that column / block
+    obj2.iloc[0] = 0
+    assert not np.shares_memory(get_array(obj2, "a"), get_array(obj, "a"))
+    tm.assert_equal(obj, obj_orig)
+
+
+@pytest.mark.parametrize("obj", [Series([1, 2], name="a"), DataFrame({"a": [1, 2]})])
+def test_to_period(using_copy_on_write, obj):
+    obj.index = Index([Timestamp("2019-12-31"), Timestamp("2020-12-31")])
+
+    obj_orig = obj.copy()
+    obj2 = obj.to_period(freq="Y")
+
+    if using_copy_on_write:
+        assert np.shares_memory(get_array(obj2, "a"), get_array(obj, "a"))
+    else:
+        assert not np.shares_memory(get_array(obj2, "a"), get_array(obj, "a"))
+
+    # mutating obj2 triggers a copy-on-write for that column / block
+    obj2.iloc[0] = 0
+    assert not np.shares_memory(get_array(obj2, "a"), get_array(obj, "a"))
+    tm.assert_equal(obj, obj_orig)
+
+
 def test_set_index(using_copy_on_write):
     # GH 49473
     df = DataFrame({"a": [1, 2, 3], "b": [4, 5, 6], "c": [0.1, 0.2, 0.3]})
diff --git a/pandas/tests/copy_view/util.py b/pandas/tests/copy_view/util.py
index 0a111e6c6cca2..b5f4f74fc7e5e 100644
--- a/pandas/tests/copy_view/util.py
+++ b/pandas/tests/copy_view/util.py
@@ -1,17 +1,20 @@
+from pandas import Series
 from pandas.core.arrays import BaseMaskedArray
 
 
-def get_array(df, col):
+def get_array(obj, col):
     """
-    Helper method to get array for a DataFrame column.
+    Helper method to get array for a DataFrame column or a Series.
 
     Equivalent of df[col].values, but without going through normal getitem,
     which triggers tracking references / CoW (and we might be testing that
     this is done by some other operation).
     """
-    icol = df.columns.get_loc(col)
+    if isinstance(obj, Series) and obj.name == col:
+        return obj._values
+    icol = obj.columns.get_loc(col)
     assert isinstance(icol, int)
-    arr = df._get_column_array(icol)
+    arr = obj._get_column_array(icol)
     if isinstance(arr, BaseMaskedArray):
         return arr._data
     return arr