diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 3992e697db7e4..55e960de5e9d1 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -119,6 +119,7 @@ Other enhancements
 - :meth:`DataFrame.explode` and :meth:`Series.explode` now support exploding of sets (:issue:`35614`)
 - `Styler` now allows direct CSS class name addition to individual data cells (:issue:`36159`)
 - :meth:`Rolling.mean()` and :meth:`Rolling.sum()` use Kahan summation to calculate the mean to avoid numerical problems (:issue:`10319`, :issue:`11645`, :issue:`13254`, :issue:`32761`, :issue:`36031`)
+- :meth:`DatetimeIndex.searchsorted`, :meth:`TimedeltaIndex.searchsorted`, :meth:`PeriodIndex.searchsorted`, and :meth:`Series.searchsorted` with datetimelike dtypes will now try to cast string arguments (listlike and scalar) to the matching datetimelike type (:issue:`36346`)
 
 .. _whatsnew_120.api_breaking.python:
 
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index e8b1c12687584..15cbdf882eb7b 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -845,8 +845,7 @@ def _validate_searchsorted_value(self, value):
         if not is_list_like(value):
             value = self._validate_scalar(value, msg, cast_str=True)
         else:
-            # TODO: cast_str?  we accept it for scalar
-            value = self._validate_listlike(value, "searchsorted")
+            value = self._validate_listlike(value, "searchsorted", cast_str=True)
 
         rv = self._unbox(value)
         return self._rebox_native(rv)
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 5ba5732c710f7..984ab49cbc517 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -178,14 +178,6 @@ def take(self, indices, axis=0, allow_fill=True, fill_value=None, **kwargs):
 
     @doc(IndexOpsMixin.searchsorted, klass="Datetime-like Index")
     def searchsorted(self, value, side="left", sorter=None):
-        if isinstance(value, str):
-            raise TypeError(
-                "searchsorted requires compatible dtype or scalar, "
-                f"not {type(value).__name__}"
-            )
-        if isinstance(value, Index):
-            value = value._data
-
         return self._data.searchsorted(value, side=side, sorter=sorter)
 
     _can_hold_na = True
diff --git a/pandas/tests/arrays/test_datetimelike.py b/pandas/tests/arrays/test_datetimelike.py
index 83b98525d3e8a..f512b168d2795 100644
--- a/pandas/tests/arrays/test_datetimelike.py
+++ b/pandas/tests/arrays/test_datetimelike.py
@@ -252,6 +252,47 @@ def test_searchsorted(self):
         else:
             assert result == 10
 
+    @pytest.mark.parametrize("box", [None, "index", "series"])
+    def test_searchsorted_castable_strings(self, arr1d, box):
+        if isinstance(arr1d, DatetimeArray):
+            tz = arr1d.tz
+            if (
+                tz is not None
+                and tz is not pytz.UTC
+                and not isinstance(tz, pytz._FixedOffset)
+            ):
+                # If we have e.g. tzutc(), when we cast to string and parse
+                #  back we get pytz.UTC, and then consider them different timezones
+                #  so incorrectly raise.
+                pytest.xfail(reason="timezone comparisons inconsistent")
+
+        arr = arr1d
+        if box is None:
+            pass
+        elif box == "index":
+            # Test the equivalent Index.searchsorted method while we're here
+            arr = self.index_cls(arr)
+        else:
+            # Test the equivalent Series.searchsorted method while we're here
+            arr = pd.Series(arr)
+
+        # scalar
+        result = arr.searchsorted(str(arr[1]))
+        assert result == 1
+
+        result = arr.searchsorted(str(arr[2]), side="right")
+        assert result == 3
+
+        result = arr.searchsorted([str(x) for x in arr[1:3]])
+        expected = np.array([1, 2], dtype=np.intp)
+        tm.assert_numpy_array_equal(result, expected)
+
+        with pytest.raises(TypeError):
+            arr.searchsorted("foo")
+
+        with pytest.raises(TypeError):
+            arr.searchsorted([str(arr[1]), "baz"])
+
     def test_getitem_2d(self, arr1d):
         # 2d slicing on a 1D array
         expected = type(arr1d)(arr1d._data[:, np.newaxis], dtype=arr1d.dtype)