The first problem with cellular phone service in Costa Rica is that it is government owned an operated. The second problem it is a monopoly. That's not the end of it either.You can't get a phone in your name unless you are a resident (and only some residents). You might have to wait 6 months or more to get a line (but many stores will happily sell you a phone). If you are not a resident or a suitable resident you will need to get a phone in someone else's name or a corporate.
If you get it in a corporation that means going to a lawyer everytime there is a problem and you need something from the "phone company". For example if someone else reports your phone stolen, you can't have it turned back on without the help of an attorney!
You might buy a phone from a private citizen who sells you the line with it. They can report it stolen and sell another phone and their line to another sucker.
On the bright side you might be able to get a half decent internet connection via your cell in Costa Rica. It used to be free, but people would charge you around US$700 to set you up!