If this is a high priced antique then I would look up a reputable repair/restoration company. You can actually make a piece worth considerably less if you don't do the restoration correctly. However, if you are not concerned about that, I would try a very high end car wax and see if that would remove the water spots. First try the wax in an inconspicuous place to make sure it doesn't remove or damage the paint.

actually try a magic eraser, don't rub hard,