diff -r 4e29c7f2b3e5 Doc/library/unittest.mock.rst
--- a/Doc/library/unittest.mock.rst	Wed Jan 11 12:00:39 2017 +0000
+++ b/Doc/library/unittest.mock.rst	Wed Jan 11 19:01:57 2017 +0200
@@ -1831,6 +1831,10 @@ sentinel
     the same attribute will always return the same object. The objects
     returned have a sensible repr so that test failure messages are readable.
 
+   .. versionchanged:: 3.7
+      The ``sentinel`` attributes now preserve their identity when they are
+      :mod:`copied <copy>` or :mod:`pickled <pickle>`.
+
 Sometimes when testing you need to test that a specific object is passed as an
 argument to another method, or returned. It can be common to create named
 sentinel objects to test this. :data:`sentinel` provides a convenient way of
diff -r 4e29c7f2b3e5 Doc/whatsnew/3.7.rst
--- a/Doc/whatsnew/3.7.rst	Wed Jan 11 12:00:39 2017 +0000
+++ b/Doc/whatsnew/3.7.rst	Wed Jan 11 19:01:57 2017 +0200
@@ -93,6 +93,13 @@ New Modules
 Improved Modules
 ================
 
+unittest.mock
+-------------
+
+The :const:`~unittest.mock.sentinel` attributes now preserve their identity
+when they are :mod:`copied <copy>` or :mod:`pickled <pickle>`.
+(Contributed by Serhiy Storchaka in :issue:`20804`.)
+
 
 Optimizations
 =============
diff -r 4e29c7f2b3e5 Lib/unittest/mock.py
--- a/Lib/unittest/mock.py	Wed Jan 11 12:00:39 2017 +0000
+++ b/Lib/unittest/mock.py	Wed Jan 11 19:01:57 2017 +0200
@@ -238,6 +238,9 @@ class _SentinelObject(object):
     def __repr__(self):
         return 'sentinel.%s' % self.name
 
+    def __reduce__(self):
+        return 'sentinel.%s' % self.name
+
 
 class _Sentinel(object):
     """Access attributes to return a named object, usable as a sentinel."""
@@ -250,6 +253,9 @@ class _Sentinel(object):
             raise AttributeError
         return self._sentinels.setdefault(name, _SentinelObject(name))
 
+    def __reduce__(self):
+        return 'sentinel'
+
 
 sentinel = _Sentinel()
 
diff -r 4e29c7f2b3e5 Lib/unittest/test/testmock/testsentinel.py
--- a/Lib/unittest/test/testmock/testsentinel.py	Wed Jan 11 12:00:39 2017 +0000
+++ b/Lib/unittest/test/testmock/testsentinel.py	Wed Jan 11 19:01:57 2017 +0200
@@ -1,4 +1,6 @@
 import unittest
+import copy
+import pickle
 from unittest.mock import sentinel, DEFAULT
 
 
@@ -23,6 +25,17 @@ class SentinelTest(unittest.TestCase):
         # If this doesn't raise an AttributeError then help(mock) is broken
         self.assertRaises(AttributeError, lambda: sentinel.__bases__)
 
+    def testPickle(self):
+        for proto in range(pickle.HIGHEST_PROTOCOL+1):
+            with self.subTest(protocol=proto):
+                pickled = pickle.dumps(sentinel.whatever, proto)
+                unpickled = pickle.loads(pickled)
+                self.assertIs(unpickled, sentinel.whatever)
+
+    def testCopy(self):
+        self.assertIs(copy.copy(sentinel.whatever), sentinel.whatever)
+        self.assertIs(copy.deepcopy(sentinel.whatever), sentinel.whatever)
+
 
 if __name__ == '__main__':
     unittest.main()