One boat a week, the D-Express (tel. 504/ 9991-0778, info [at] hondurasdivers [dot] com), plies the waters between Placencia, Belize, and Puerto Cortés [1], charging US$53 for the 2–3-hour trip.
Links:
[1] http://www.moon.com/destinations/honduras/the-north-coast/puerto-cortes