The Roatán Institute for Marine Sciences sits inside Anthony's Key Resort on Sandy Bay and runs the most-visited attraction on the island that isn't a beach: a bottlenose dolphin encounter in a large fenced sea-lagoon. Programmes range from a half-hour wade in the shallows ("Encounter") to a 30-minute open-water swim with the dolphins, to longer "Trainer for a Day" packages.
Captive dolphin programmes are ethically contested; RIMS is at the more research- and conservation-oriented end of the spectrum but is still a marine park. Whatever your view, the encounter sells out months in advance through the cruise season — book direct on the resort website rather than via the cruise lines for cheaper rates.