When I was on the Fantasy last June doing the eastern Caribbean cruise, I purchased the 'global data package' from Verizon with my iPhone 5. When talking with the Verizon reps when adding it to my plan, they said that it would work on the ship when the 'cellular at sea' system was turned on and at St. Maarten and St. Thomas.
Well on the ship when not in port, I was able to send and receive text massages, get phone calls but no data would work. When in ports, the data worked as well as the others.
The nice thing with Verizon is every time you roam and get onto a new network, they will send you a free text message explaining the text, voice, and data rates. However, you need to turn you cellular services to do that (you can leave your data off) so if you have any text messages waiting to come in, they will and you get billed at that rate.
My parents have TMobile and in St. Thomas they were able to user their phones just like they've were at home in Ohio. No extra charges or anything. I am not sure about Verizon as I had the Global Data Plan.
Hope that helps.