For service in any foreign ports, you have to ask your cell provider is they do international service. Most don't, some do, and some are adding it on.
Unless it is a satellite phone, once you are a few miles away from land, don't expect service. There is no cell service onboard. You do have phones, that have expensive ship to shore rates and an emergency number to give the family to call you. 1-888-dc-at-sea (322-8732)
Keep in mind Key West is not a foreign port. At least right now.(inside joke, ask a KW native, you'll get a good story!)
Some people have reported cell ability at CC, some not. Again falls under the international calling rules of your cell provider.