Whisk the vinegar, honey, oil, and garlic in a bowl. Arrange halibuts in an 8-inch square baking dish. Pour marinade over the fish, coating it completely. Cover and refrigerate at least 30 minutes and up to 4 hours.
Preheat the broiler. Line the bottom and sides of a baking sheet with foil. Spray the foil with nonstick cooking spray. Remove fish from marinade, reserving marinade, and arrange the fillets atop the baking sheet. Pour the marinade into a heavy small saucepan. Broil the fillets until they are just cooked through and caramelized on top, about 12 minutes.
Meanwhile bring the marinade to a boil and simmer until it thickens slightly and becomes syrupy, whisking often, about 15 minutes. Spoon off any excess oil from the sauce, if desired.
Transfer the fillets to plates. Spoon the sauce over and around the fillets, and serve.