Definitely check with your cruise line about the specific ship you'll be on. They should have the name of the provider and compatibility info somewhere. Then go check the provider and see their costs, don;t take anyone on the ships work for it.
I went on a Royal Carribean a couple of years ago and they did have service available (provided by ATT IIRC, I'm not sure if it covered Verizon also), but the cost was similar to overseas roaming, which was outrageously expensive. I ended up turing data roaming off and kept airplane mode switched on except when we docked at Key West.
The ship also provded WiFi in some areas but it also was not free, though this also varies by line and ship.