diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index ee9b948a76ac8..b1463f52333a1 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -18,7 +18,7 @@
 
 from pandas.core.dtypes.common import _NS_DTYPE, is_float, is_integer, is_scalar
 from pandas.core.dtypes.dtypes import DatetimeTZDtype
-from pandas.core.dtypes.missing import isna
+from pandas.core.dtypes.missing import is_valid_nat_for_dtype
 
 from pandas.core.accessor import delegate_names
 from pandas.core.arrays.datetimes import (
@@ -677,8 +677,8 @@ def get_loc(self, key, method=None, tolerance=None):
         -------
         loc : int
         """
-        if is_scalar(key) and isna(key):
-            key = NaT  # FIXME: do this systematically
+        if is_valid_nat_for_dtype(key, self.dtype):
+            key = NaT
 
         if tolerance is not None:
             # try converting tolerance now, so errors don't get swallowed by
diff --git a/pandas/core/indexes/numeric.py b/pandas/core/indexes/numeric.py
index 465f21da1278a..14cb061aa012c 100644
--- a/pandas/core/indexes/numeric.py
+++ b/pandas/core/indexes/numeric.py
@@ -433,11 +433,7 @@ def get_value(self, series: "Series", key):
             raise InvalidIndexError
 
         loc = self.get_loc(key)
-        if not is_scalar(loc):
-            return series.iloc[loc]
-
-        new_values = series._values[loc]
-        return new_values
+        return self._get_values_for_loc(series, loc)
 
     def equals(self, other) -> bool:
         """
diff --git a/pandas/tests/indexes/datetimes/test_indexing.py b/pandas/tests/indexes/datetimes/test_indexing.py
index f3c255d50aba1..26d99da42cd2b 100644
--- a/pandas/tests/indexes/datetimes/test_indexing.py
+++ b/pandas/tests/indexes/datetimes/test_indexing.py
@@ -773,3 +773,14 @@ def test_get_loc_nat(self):
         # GH#20464
         index = DatetimeIndex(["1/3/2000", "NaT"])
         assert index.get_loc(pd.NaT) == 1
+
+        assert index.get_loc(None) == 1
+
+        assert index.get_loc(np.nan) == 1
+
+        assert index.get_loc(pd.NA) == 1
+
+        assert index.get_loc(np.datetime64("NaT")) == 1
+
+        with pytest.raises(KeyError, match="NaT"):
+            index.get_loc(np.timedelta64("NaT"))
diff --git a/pandas/tests/indexes/test_numeric.py b/pandas/tests/indexes/test_numeric.py
index 12cc51222e6bb..b83ceb1ce699c 100644
--- a/pandas/tests/indexes/test_numeric.py
+++ b/pandas/tests/indexes/test_numeric.py
@@ -393,6 +393,46 @@ def test_get_loc_missing_nan(self):
             # listlike/non-hashable raises TypeError
             idx.get_loc([np.nan])
 
+    @pytest.mark.parametrize(
+        "vals",
+        [
+            pd.date_range("2016-01-01", periods=3),
+            pd.timedelta_range("1 Day", periods=3),
+        ],
+    )
+    def test_lookups_datetimelike_values(self, vals):
+        # If we have datetime64 or timedelta64 values, make sure they are
+        #  wrappped correctly
+        ser = pd.Series(vals, index=range(3, 6))
+        ser.index = ser.index.astype("float64")
+
+        expected = vals[1]
+
+        result = ser.index.get_value(ser, 4.0)
+        assert isinstance(result, type(expected)) and result == expected
+        result = ser.index.get_value(ser, 4)
+        assert isinstance(result, type(expected)) and result == expected
+
+        result = ser[4.0]
+        assert isinstance(result, type(expected)) and result == expected
+        result = ser[4]
+        assert isinstance(result, type(expected)) and result == expected
+
+        result = ser.loc[4.0]
+        assert isinstance(result, type(expected)) and result == expected
+        result = ser.loc[4]
+        assert isinstance(result, type(expected)) and result == expected
+
+        result = ser.at[4.0]
+        assert isinstance(result, type(expected)) and result == expected
+        # Note: ser.at[4] raises ValueError; TODO: should we make this match loc?
+
+        result = ser.iloc[1]
+        assert isinstance(result, type(expected)) and result == expected
+
+        result = ser.iat[1]
+        assert isinstance(result, type(expected)) and result == expected
+
     def test_contains_nans(self):
         i = Float64Index([1.0, 2.0, np.nan])
         assert np.nan in i