There is service available for CDMA phones (Verizon's & Sprint's technology) on Grand Cayman. Eric advised of the cost. Coverage is OK in the Seven Mile Beach and Rum Point areas, a bit spotty elsewhere and almost non-existent on the East End. I believe data plans do not work unless you have a "world phone".
The local carriers, LIME and Digicell, primarily use the GSM technology adopted by T-Mobile and AT&T, so coverage with those phones is generally better island-wide (It is the only coverage on the Sister Islands).
If you plan on using your phone a lot, it may make sense to rent or buy an unlocked GSM phone prior to or during your visit. With an unlocked GSM phone you can then purchase a pre-paid SIM card from one of the local carriers for cheaper international calling rates.
