Belmopan ? Unless you are headed to Guatemala, it's out of the way, not on the way. Maybe you meant Belize City?
Anyway you can go from San Pedro to Chetumal direct by boat. Nice trip, quick and easy.
To go to Honduras you'll need to go to BC and catch a flight, or find your way down to PG and catch a boat.
To go to Guatemala - head over to the mainland, get on the western highway and go straight west til you hit the boarder.