diff --git a/certbot/certbot/_internal/ocsp.py b/certbot/certbot/_internal/ocsp.py
index d16aea918..300639b19 100644
--- a/certbot/certbot/_internal/ocsp.py
+++ b/certbot/certbot/_internal/ocsp.py
@@ -21,7 +21,6 @@ from acme.magic_typing import Tuple  # pylint: disable=unused-import, no-name-in
 from certbot import crypto_util
 from certbot import errors
 from certbot import util
-from certbot._internal.storage import RenewableCert  # pylint: disable=unused-import
 
 try:
     # Only cryptography>=2.5 has ocsp module
@@ -32,7 +31,6 @@ except (ImportError, AttributeError):  # pragma: no cover
     ocsp = None  # type: ignore
 
 
-
 logger = logging.getLogger(__name__)
 
 
@@ -112,34 +110,9 @@ class RevocationChecker(object):
         """
 
         if self.use_openssl_binary:
-            return self._ocsp_times_openssl_bin(response_file)
+            return _ocsp_times_openssl_bin(response_file)
         return _ocsp_times_cryptography(response_file)
 
-    def _ocsp_times_openssl_bin(self, response_file):
-        """
-        Reads OCSP response file using OpenSSL binary and returns
-        producedAt, thisUpdate and nextUpdate values in datetime format.
-
-        :param str response_file: File path to OCSP response
-
-        :returns: tuple of producedAt, thisUpdate and nextUpdate values
-        :rtype: tuple of datetime
-        """
-        cmd = ["openssl", "ocsp", "-resp_text", "-noverify", "-respin", response_file]
-        logger.debug("Reading OCSP response from temp file: %s", response_file)
-        logger.debug(" ".join(cmd))
-        try:
-            output, err = util.run_script(cmd, log=logger.debug)
-        except errors.SubprocessError:
-            logger.info("Reading OCSP response from file failed.")
-            return None, None, None
-
-        prod_str, this_str, next_str = _translate_ocsp_response_times(output)
-        prod_dt = util.parse_datetime(prod_str)
-        this_dt = util.parse_datetime(this_str)
-        next_dt = util.parse_datetime(next_str)
-        return prod_dt, this_dt, next_dt
-
     def _check_ocsp_openssl_bin(self, cert_path, chain_path, host, url, response_file=None):
         # type: (str, str, str, str, Optional[str]) -> bool
         # jdkasten thanks "Bulletproof SSL and TLS - Ivan Ristic" for documenting this!
@@ -195,10 +168,37 @@ def _determine_ocsp_server(cert_path):
     return None, None
 
 
+def _ocsp_times_openssl_bin(response_file):
+    """
+    Reads OCSP response file using OpenSSL binary and returns
+    producedAt, thisUpdate and nextUpdate values in datetime format.
+
+    :param str response_file: File path to OCSP response
+
+    :returns: tuple of producedAt, thisUpdate and nextUpdate values
+    :rtype: tuple of datetime
+    """
+    cmd = ["openssl", "ocsp", "-resp_text", "-noverify", "-respin", response_file]
+    logger.debug("Reading OCSP response from temp file: %s", response_file)
+    logger.debug(" ".join(cmd))
+    try:
+        output, err = util.run_script(cmd, log=logger.debug)
+    except errors.SubprocessError:
+        logger.info("Reading OCSP response from file failed.")
+        return None, None, None
+
+    prod_str, this_str, next_str = _translate_ocsp_response_times(output)
+    prod_dt = util.parse_datetime(prod_str)
+    this_dt = util.parse_datetime(this_str)
+    next_dt = util.parse_datetime(next_str)
+    return prod_dt, this_dt, next_dt
+
+
 def _ocsp_times_cryptography(response_file):
     """
     Reads OCSP response using cryptography and returns producedAt,
-    thisUpdate and nextUpdate values in datetime format.
+    thisUpdate and nextUpdate values in datetime format, or None
+    if the file cannot be opened.
 
     :param str response_file: File path to OCSP response
 
@@ -206,8 +206,11 @@ def _ocsp_times_cryptography(response_file):
     :rtype: tuple of datetime
     """
 
-    with open(response_file, 'rb') as fh:
-        raw_response = fh.read()
+    try:
+        with open(response_file, 'rb') as fh:
+            raw_response = fh.read()
+    except OSError:
+        return None, None, None
 
     response = ocsp.load_der_ocsp_response(raw_response)
     return response.produced_at, response.this_update, response.next_update
@@ -371,7 +374,7 @@ def _translate_ocsp_query(cert_path, ocsp_output, ocsp_errors):
         return True
     else:
         logger.warning("Unable to properly parse OCSP output: %s\nstderr:%s",
-                    ocsp_output, ocsp_errors)
+                       ocsp_output, ocsp_errors)
         return False
 
 
diff --git a/certbot/tests/ocsp_test.py b/certbot/tests/ocsp_test.py
index b550546c0..9f298a365 100644
--- a/certbot/tests/ocsp_test.py
+++ b/certbot/tests/ocsp_test.py
@@ -137,6 +137,32 @@ class OCSPTestOpenSSL(unittest.TestCase):
         self.assertEqual(ocsp._translate_ocsp_query(*openssl_expired_ocsp_revoked), True)
         self.assertEqual(mock_log.info.call_count, 1)
 
+    @mock.patch('certbot.util.run_script')
+    def test_ocsp_response_get_times(self, mock_run):
+        mock_run.return_value = ocsp_times_example
+        producedAt, thisUpdate, nextUpdate = self.checker.ocsp_times("mocked")
+        self.assertEqual(producedAt, datetime(2020, 1, 24, 11, 10))
+        self.assertEqual(thisUpdate, datetime(2020, 1, 24, 11, 0))
+        self.assertEqual(nextUpdate, datetime(2020, 1, 31, 11, 0))
+
+    @mock.patch('certbot.util.run_script')
+    def test_ocsp_response_get_times_badoutput(self, mock_run):
+        mock_run.return_value = ("Something unparsable", "")
+        producedAt, thisUpdate, nextUpdate = self.checker.ocsp_times("mocked")
+        self.assertEqual(producedAt, None)
+        self.assertEqual(thisUpdate, None)
+        self.assertEqual(nextUpdate, None)
+
+    @mock.patch('certbot._internal.ocsp.logger')
+    @mock.patch('certbot.util.run_script')
+    def test_ocsp_response_get_times_error(self, mock_run, mock_log):
+        mock_run.side_effect = errors.SubprocessError
+        producedAt, thisUpdate, nextUpdate = self.checker.ocsp_times("mocked")
+        self.assertEqual(producedAt, None)
+        self.assertEqual(thisUpdate, None)
+        self.assertEqual(nextUpdate, None)
+        self.assertEqual(mock_log.info.call_count, 1)
+
 
 @unittest.skipIf(not ocsp_lib,
                  reason='This class tests functionalities available only on cryptography>=2.5.0')
@@ -278,6 +304,26 @@ class OSCPTestCryptography(unittest.TestCase):
                     revoked = self.checker.ocsp_revoked(self.cert_obj)
         self.assertFalse(revoked)
 
+    def test_ocsp_times_cryptography(self):
+        with mock.patch('certbot._internal.ocsp.open', mock.mock_open(read_data="")):
+            with mock.patch('cryptography.x509.ocsp.load_der_ocsp_response') as mock_load:
+                resp = mock.MagicMock()
+                resp.produced_at = datetime(2020, 1, 2, 9, 9)
+                resp.this_update = datetime(2020, 1, 2, 8, 8)
+                resp.next_update = datetime(2020, 1, 3, 4, 4)
+                mock_load.return_value = resp
+
+                produced_at, this_update, next_update = self.checker.ocsp_times("mocked")
+                self.assertEqual(produced_at, datetime(2020, 1, 2, 9, 9))
+                self.assertEqual(this_update, datetime(2020, 1, 2, 8, 8))
+                self.assertEqual(next_update, datetime(2020, 1, 3, 4, 4))
+
+    def test_ocsp_times_cryptography_error(self):
+        with mock.patch('certbot._internal.ocsp.open', mock.mock_open(read_data="")) as mock_open:
+            mock_open.side_effect = OSError
+            produced_at, this_update, next_update = self.checker.ocsp_times("mocked")
+            self.assertEqual([produced_at, this_update, next_update], [None, None, None])
+
 
 @contextlib.contextmanager
 def _ocsp_mock(certificate_status, response_status,
@@ -377,6 +423,12 @@ revoked
 """,
 """Response verify OK""")
 
+ocsp_times_example = ("""
+    Produced At: Jan 24 11:10:00 2020 GMT
+    This Update: Jan 24 11:00:00 2020 GMT
+    Next Update: Jan 31 11:00:00 2020 GMT
+""", "")
+
 
 if __name__ == '__main__':
     unittest.main()  # pragma: no cover