diff --git a/sunpy/time/tests/test_time.py b/sunpy/time/tests/test_time.py
index 73736ce8208..ce26ed290ca 100644
--- a/sunpy/time/tests/test_time.py
+++ b/sunpy/time/tests/test_time.py
@@ -135,7 +135,8 @@ def test_parse_time_individual_numpy_datetime():
 
 
 def test_parse_time_numpy_datetime_timezone():
-    dt64 = np.datetime64('2014-02-07T16:47:51-0500')
+    with pytest.warns(DeprecationWarning, match='parsing timezone aware datetimes is deprecated'):
+        dt64 = np.datetime64('2014-02-07T16:47:51-0500')
     dt = parse_time(dt64)
 
     assert dt == Time('2014-02-07T21:47:51', format='isot')
@@ -251,7 +252,6 @@ def test_parse_time_leap_second():
     (63072064.184, 'cxcsec'),
     (datetime(2000, 1, 2, 12, 0, 0), 'datetime'),
     (2000.45, 'decimalyear'),
-    ('2000-01-01T00:00:00.000(TAI)', 'fits'),
     (630720013.0, 'gps'),
     ('2000-01-01 00:00:00.000', 'iso'),
     ('2000-01-01T00:00:00.000', 'isot'),
diff --git a/sunpy/time/tests/test_timerange.py b/sunpy/time/tests/test_timerange.py
index 3ae73e2d5f3..6c7c39fb8cd 100644
--- a/sunpy/time/tests/test_timerange.py
+++ b/sunpy/time/tests/test_timerange.py
@@ -4,6 +4,7 @@
 
 import astropy.units as u
 from astropy.time import Time, TimeDelta
+from astropy.utils.exceptions import ErfaWarning
 
 import sunpy.time
 from sunpy.time import is_time_equal
@@ -258,6 +259,7 @@ def test_contains(timerange_a):
     assert timerange.end in timerange
     assert '2014/05/04 15:21' in timerange
     assert '1975/4/13' not in timerange
-    assert '2100/1/1'not in timerange
+    with pytest.warns(ErfaWarning, match='dubious year'):
+        assert '2100/1/1'not in timerange
     assert '2014/05/03 12:00' in timerange
     assert '2014/05/05 21:00' in timerange