diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index f6e90a3341424..01ad7d69cddc7 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -378,6 +378,7 @@ Categorical
 Datetimelike
 ^^^^^^^^^^^^
 - Bug in :class:`DataFrame` constructor unnecessarily copying non-datetimelike 2D object arrays (:issue:`39272`)
+- Bug in :func:`to_datetime` with ``format`` and ``pandas.NA`` was raising ``ValueError`` (:issue:`42957`)
 - :func:`to_datetime` would silently swap ``MM/DD/YYYY`` and ``DD/MM/YYYY`` formats if the given ``dayfirst`` option could not be respected - now, a warning is raised in the case of delimited date strings (e.g. ``31-12-2012``) (:issue:`12585`)
 -
 
diff --git a/pandas/_libs/tslibs/strptime.pyx b/pandas/_libs/tslibs/strptime.pyx
index e7fb38db2aa17..d214694fb659d 100644
--- a/pandas/_libs/tslibs/strptime.pyx
+++ b/pandas/_libs/tslibs/strptime.pyx
@@ -20,10 +20,10 @@ from numpy cimport (
     ndarray,
 )
 
+from pandas._libs.missing cimport checknull_with_nat_and_na
 from pandas._libs.tslibs.nattype cimport (
     NPY_NAT,
     c_nat_strings as nat_strings,
-    checknull_with_nat,
 )
 from pandas._libs.tslibs.np_datetime cimport (
     check_dts_bounds,
@@ -134,7 +134,7 @@ def array_strptime(ndarray[object] values, object fmt, bint exact=True, errors='
                 iresult[i] = NPY_NAT
                 continue
         else:
-            if checknull_with_nat(val):
+            if checknull_with_nat_and_na(val):
                 iresult[i] = NPY_NAT
                 continue
             else:
diff --git a/pandas/tests/tools/test_to_datetime.py b/pandas/tests/tools/test_to_datetime.py
index a38affbc7f723..850ce6df21b7f 100644
--- a/pandas/tests/tools/test_to_datetime.py
+++ b/pandas/tests/tools/test_to_datetime.py
@@ -177,6 +177,28 @@ def test_to_datetime_format_YYYYMMDD_overflow(self, input_s, expected):
         result = to_datetime(input_s, format="%Y%m%d", errors="coerce")
         tm.assert_series_equal(result, expected)
 
+    @pytest.mark.parametrize(
+        "data, format, expected",
+        [
+            ([pd.NA], "%Y%m%d%H%M%S", DatetimeIndex(["NaT"])),
+            ([pd.NA], None, DatetimeIndex(["NaT"])),
+            (
+                [pd.NA, "20210202202020"],
+                "%Y%m%d%H%M%S",
+                DatetimeIndex(["NaT", "2021-02-02 20:20:20"]),
+            ),
+            (["201010", pd.NA], "%y%m%d", DatetimeIndex(["2020-10-10", "NaT"])),
+            (["201010", pd.NA], "%d%m%y", DatetimeIndex(["2010-10-20", "NaT"])),
+            (["201010", pd.NA], None, DatetimeIndex(["2010-10-20", "NaT"])),
+            ([None, np.nan, pd.NA], None, DatetimeIndex(["NaT", "NaT", "NaT"])),
+            ([None, np.nan, pd.NA], "%Y%m%d", DatetimeIndex(["NaT", "NaT", "NaT"])),
+        ],
+    )
+    def test_to_datetime_with_NA(self, data, format, expected):
+        # GH#42957
+        result = to_datetime(data, format=format)
+        tm.assert_index_equal(result, expected)
+
     @pytest.mark.parametrize("cache", [True, False])
     def test_to_datetime_format_integer(self, cache):
         # GH 10178