There are 2 dentists, located in Belize City that are always highly recommended.
My family uses Dr. Pedro Habet of The Dental Center www.thedentalcenter.bz
He is a qualified orthodontist.
And there is the Heusner's Professional Dentistry clinic - Dr Adrian Heusner. I am unsure if he is an orthodontist but he is certainly popular and produces nice results.
Don't use Dr. Franklin Hernandez in San Pedro, he claims to be an orthodontist but he isn't.