Cats do tear up, but not for reasons like our own. Cats shed tears in response to discomfort or eye irritants and not from emotional distress. Cats communicate their emotions differently. They do not weep in sorrow and bawl like we do. What could happen is that your cat would be vocalizing a sad meow instead.
Should you notice that your cat tears up often, you should check if its present living conditions may contribute to it. Dust or even the types of cleaning chemicals used in your home may cause some irritation. Should it continue or if you believe that it may be due to a medical issue your cat has, bring it to the veterinarian to have it checked out.