You may have to sacrifice one to save the other. Put a groove in the bottom edge of the lower one with a nail file, then tap FIRMLY on the bench to shatter it. If you are holding the top one, it should be unharmed. A teatowel on the bench may help corral the shards for disposal. Rubber gloves as per StudSpud's comment are a very good idea.
Put them on the bench with a towel underneath and put a bag of frozen peas (still in the bag) in the top bowl, wait until the top bowl is cold on the outside, then turn them on the side and give them a firm but gentle tap on top of the towel.
Staff at personal devices shop: Welcome! How can I help you?
AJ: I'd like a massage device that vibrates.
Staff: Any preference for size and shape?
AJ: Something gentle. It's for my bowls who love each other too much.
Edit: just saw Seagoon already mentioned this. Oh well, guess you now own a double walled bowl, or two less bowls, depending on what you decide to do. Welcome to a fork in the road of your life.