According to an article from the Virginian Pilot from 2002, there is cell coverage on base. You might want to find someone who was stationed there recently to find out more.
when I was there they had GTMO cell phones that only worked on the base for base phones...They did not have any other cell phone coverage...My unit had a satellite phone that we were able to use...They have a decent phone card rate as well...When I was there in 04 the rate was ridiculous...They got a new contract in 06 and if I remember correctly it was around 5 cents a minute...
I was there in 05 and I do recall a few of the guys had a cell phone through a private network on base, but it was expensive and it did not always work. Phone cards were alright, but the phone banks are always tied. The other option you have is the computer. I remember using some program where you logged on and could talk to people through the computer. It was cheap and easy. All you need is a two way headphone. Good Luck!