diff --git a/sklearn/tests/test_common.py b/sklearn/tests/test_common.py
index 92cbed36044bf..af98c1bc50a74 100644
--- a/sklearn/tests/test_common.py
+++ b/sklearn/tests/test_common.py
@@ -31,6 +31,7 @@
 from sklearn.utils import IS_PYPY
 from sklearn.utils._testing import SkipTest
 from sklearn.utils.estimator_checks import (
+    _mark_xfail_checks,
     _construct_instance,
     _set_checking_parameters,
     _set_check_estimator_ids,
@@ -47,6 +48,24 @@ def test_all_estimator_no_base_class():
         assert not name.lower().startswith('base'), msg
 
 
+def test_estimator_cls_parameterize_with_checks():
+    # Non-regression test for #16707 to ensure that parametrize_with_checks
+    # works with estimator classes
+    param_checks = parametrize_with_checks([LogisticRegression])
+    # Using the generator does not raise
+    list(param_checks.args[1])
+
+
+def test_mark_xfail_checks_with_unconsructable_estimator():
+    class MyEstimator:
+        def __init__(self):
+            raise ValueError("This is bad")
+
+    estimator, check = _mark_xfail_checks(MyEstimator, 42, None)
+    assert estimator == MyEstimator
+    assert check == 42
+
+
 @pytest.mark.parametrize(
         'name, Estimator',
         all_estimators()
diff --git a/sklearn/utils/estimator_checks.py b/sklearn/utils/estimator_checks.py
index 2cfb06c7994db..34a0e25c7fcaa 100644
--- a/sklearn/utils/estimator_checks.py
+++ b/sklearn/utils/estimator_checks.py
@@ -360,8 +360,17 @@ def _generate_class_checks(Estimator):
 
 def _mark_xfail_checks(estimator, check, pytest):
     """Mark estimator check pairs with xfail"""
+    if isinstance(estimator, type):
+        # try to construct estimator to get tags, if it is unable to then
+        # return the estimator class
+        try:
+            xfail_checks = _safe_tags(_construct_instance(estimator),
+                                      '_xfail_test')
+        except Exception:
+            return estimator, check
+    else:
+        xfail_checks = _safe_tags(estimator, '_xfail_test')
 
-    xfail_checks = _safe_tags(estimator, '_xfail_test')
     if not xfail_checks:
         return estimator, check