diff --git a/src/microdot/microdot.py b/src/microdot/microdot.py
index 0341583..49128ad 100644
--- a/src/microdot/microdot.py
+++ b/src/microdot/microdot.py
@@ -598,7 +598,7 @@ class Response:
             else:  # pragma: no cover
                 http_cookie += '; Expires=' + time.strftime(
                     '%a, %d %b %Y %H:%M:%S GMT', expires.timetuple())
-        if max_age:
+        if max_age is not None:
             http_cookie += '; Max-Age=' + str(max_age)
         if secure:
             http_cookie += '; Secure'
@@ -616,10 +616,10 @@ class Response:
 
         :param cookie: The cookie's name.
         :param kwargs: Any cookie opens and flags supported by
-                       ``set_cookie()`` except ``expires``.
+                       ``set_cookie()`` except ``expires`` and ``max_age``.
         """
         self.set_cookie(cookie, '', expires='Thu, 01 Jan 1970 00:00:01 GMT',
-                        **kwargs)
+                        max_age=0, **kwargs)
 
     def complete(self):
         if isinstance(self.body, bytes) and \
diff --git a/src/microdot/test_client.py b/src/microdot/test_client.py
index 4ae83d8..fcc5a9c 100644
--- a/src/microdot/test_client.py
+++ b/src/microdot/test_client.py
@@ -141,7 +141,17 @@ class TestClient:
             cookie_options = cookie_value.split(';')
             delete = False
             for option in cookie_options[1:]:
-                if option.strip().lower().startswith('expires='):
+                if option.strip().lower().startswith(
+                        'max-age='):  # pragma: no cover
+                    _, age = option.strip().split('=', 1)
+                    try:
+                        age = int(age)
+                    except ValueError:  # pragma: no cover
+                        age = 0
+                    if age <= 0:
+                        delete = True
+                        break
+                elif option.strip().lower().startswith('expires='):
                     _, e = option.strip().split('=', 1)
                     # this is a very limited parser for cookie expiry
                     # that only detects a cookie deletion request when
diff --git a/tests/test_response.py b/tests/test_response.py
index 1fdae2b..ae2f4c4 100644
--- a/tests/test_response.py
+++ b/tests/test_response.py
@@ -203,7 +203,8 @@ class TestResponse(unittest.TestCase):
             'foo7=bar7; Path=/foo; Domain=example.com:1234; '
             'Expires=Tue, 05 Nov 2019 02:23:54 GMT; Max-Age=123; Secure; '
             'HttpOnly',
-            'foo8=; Expires=Thu, 01 Jan 1970 00:00:01 GMT; HttpOnly',
+            ('foo8=; Expires=Thu, 01 Jan 1970 00:00:01 GMT; Max-Age=0; '
+             'HttpOnly'),
         ]})
 
     def test_redirect(self):