I went through this in February while preparing for a visit to San Pedro. Verizon advised me they would charge me $2.89 a minute to "roam" using my smart phone in Belize. I researched getting a local sim card to use in an old unlocked GSM phone I keep for traveling, but the cost savings wasn't that significant and there are a whole lot of hoops to jump through. What I ended up doing was renting a Digicell phone from Quicksilver while I was in Belize. Their representative met me at the airport in AC and after some simple paperwork I was good to go. It wasn't a smart phone, but I didn't mind as I just needed it to make and receive voice calls. The cost savings was significant. I can't remember the airtime rate, but I remember spending about $70 for the rental fee and airtime while I was there. I calculated the same usage with my Verizon phone would have been over $200.
Just my experience. I hope it helps.