diff --git a/astropy/coordinates/tests/test_matching.py b/astropy/coordinates/tests/test_matching.py
index e0f9f1a79a76..248b78c7ca06 100644
--- a/astropy/coordinates/tests/test_matching.py
+++ b/astropy/coordinates/tests/test_matching.py
@@ -167,7 +167,7 @@ def test_search_around():
     idx1_0p05deg, idx2_0p05deg, d2d_0p05deg, d3d_0p05deg = search_around_sky(coo1, coo2, 0.05*u.deg)
 
     assert list(zip(idx1_1deg, idx2_1deg)) == [(0, 2), (0, 3), (1, 1), (1, 2)]
-    assert d2d_1deg[0] == 1.0*u.deg
+    assert_allclose(d2d_1deg[0], 1.0*u.deg, atol=1e-14*u.deg, rtol=0)
     assert_allclose(d2d_1deg, [1, 0, .1, .9]*u.deg)
 
     assert list(zip(idx1_0p05deg, idx2_0p05deg)) == [(0, 3)]
diff --git a/astropy/coordinates/tests/test_sky_coord.py b/astropy/coordinates/tests/test_sky_coord.py
index 47619f6a24e2..f413d20a3519 100644
--- a/astropy/coordinates/tests/test_sky_coord.py
+++ b/astropy/coordinates/tests/test_sky_coord.py
@@ -1886,10 +1886,10 @@ def test_match_to_catalog_3d_and_sky():
 
     idx, angle, quantity = cfk5_J1950.match_to_catalog_3d(cfk5_default)
     npt.assert_array_equal(idx, [0, 1, 2, 3])
-    assert_allclose(angle, 0*u.deg, atol=1e-15*u.deg, rtol=0)
+    assert_allclose(angle, 0*u.deg, atol=2e-15*u.deg, rtol=0)
     assert_allclose(quantity, 0*u.kpc, atol=1e-15*u.kpc, rtol=0)
 
     idx, angle, distance = cfk5_J1950.match_to_catalog_sky(cfk5_default)
     npt.assert_array_equal(idx, [0, 1, 2, 3])
-    assert_allclose(angle, 0 * u.deg, atol=1e-15*u.deg, rtol=0)
-    assert_allclose(distance, 0*u.kpc, atol=1e-15*u.kpc, rtol=0)
+    assert_allclose(angle, 0 * u.deg, atol=2e-15*u.deg, rtol=0)
+    assert_allclose(distance, 0*u.kpc, atol=2e-15*u.kpc, rtol=0)