diff --git a/pandas/tests/frame/test_dtypes.py b/pandas/tests/frame/test_dtypes.py
index b37bf02a6b8e7..ca54993712439 100644
--- a/pandas/tests/frame/test_dtypes.py
+++ b/pandas/tests/frame/test_dtypes.py
@@ -808,11 +808,15 @@ def test_astype_to_incorrect_datetimelike(self, unit):
         other = "m8[{}]".format(unit)
 
         df = DataFrame(np.array([[1, 2, 3]], dtype=dtype))
-        with pytest.raises(TypeError):
+        msg = (r"cannot astype a datetimelike from \[datetime64\[ns\]\] to"
+               r" \[timedelta64\[{}\]\]").format(unit)
+        with pytest.raises(TypeError, match=msg):
             df.astype(other)
 
+        msg = (r"cannot astype a timedelta from \[timedelta64\[ns\]\] to"
+               r" \[datetime64\[{}\]\]").format(unit)
         df = DataFrame(np.array([[1, 2, 3]], dtype=other))
-        with pytest.raises(TypeError):
+        with pytest.raises(TypeError, match=msg):
             df.astype(dtype)
 
     def test_timedeltas(self):
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index 8525b877618c9..96e18c6a60cac 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -683,17 +683,44 @@ def test_constructor_dtype_datetime64(self):
         assert s.dtype == 'M8[ns]'
 
         # GH3414 related
-        # msg = (r"cannot astype a datetimelike from \[datetime64\[ns\]\] to"
-        #        r" \[int32\]")
-        # with pytest.raises(TypeError, match=msg):
-        #     Series(Series(dates).astype('int') / 1000000, dtype='M8[ms]')
-        pytest.raises(TypeError, lambda x: Series(
-            Series(dates).astype('int') / 1000000, dtype='M8[ms]'))
-
-        msg = (r"The 'datetime64' dtype has no unit\. Please pass in"
-               r" 'datetime64\[ns\]' instead\.")
-        with pytest.raises(ValueError, match=msg):
-            Series(dates, dtype='datetime64')
+        expected = Series([
+            datetime(2013, 1, 1),
+            datetime(2013, 1, 2),
+            datetime(2013, 1, 3),
+        ], dtype='datetime64[ns]')
+
+        result = Series(
+            Series(dates).astype(np.int64) / 1000000, dtype='M8[ms]')
+        tm.assert_series_equal(result, expected)
+
+        result = Series(dates, dtype='datetime64[ns]')
+        tm.assert_series_equal(result, expected)
+
+        expected = Series([
+            pd.NaT,
+            datetime(2013, 1, 2),
+            datetime(2013, 1, 3),
+        ], dtype='datetime64[ns]')
+        result = Series([np.nan] + dates[1:], dtype='datetime64[ns]')
+        tm.assert_series_equal(result, expected)
+
+        dts = Series(dates, dtype='datetime64[ns]')
+
+        # valid astype
+        dts.astype('int64')
+
+        # invalid casting
+        msg = (r"cannot astype a datetimelike from \[datetime64\[ns\]\] to"
+               r" \[int32\]")
+        with pytest.raises(TypeError, match=msg):
+            dts.astype('int32')
+
+        # ints are ok
+        # we test with np.int64 to get similar results on
+        # windows / 32-bit platforms
+        result = Series(dts, dtype=np.int64)
+        expected = Series(dts.astype(np.int64))
+        tm.assert_series_equal(result, expected)
 
         # invalid dates can be help as object
         result = Series([datetime(2, 1, 1)])
diff --git a/pandas/tests/series/test_dtypes.py b/pandas/tests/series/test_dtypes.py
index d8046c4944afc..735b8553b14d3 100644
--- a/pandas/tests/series/test_dtypes.py
+++ b/pandas/tests/series/test_dtypes.py
@@ -415,7 +415,9 @@ def test_astype_generic_timestamp_no_frequency(self, dtype):
         data = [1]
         s = Series(data)
 
-        msg = "dtype has no unit. Please pass in"
+        msg = ((r"The '{dtype}' dtype has no unit\. "
+                r"Please pass in '{dtype}\[ns\]' instead.")
+               .format(dtype=dtype.__name__))
         with pytest.raises(ValueError, match=msg):
             s.astype(dtype)