In a sauce pan over a low heat, warm the key lime jelly just until it becomes like a thick syrup.
Salt and pepper the swordfish steaks. Brush or spoon the key lime jelly onto the steaks reserving some for the opposite side while grilling.
Place the swordfish onto the grill on high heat for 2 minutes. Turn the steaks then add additional jelly to the opposite side. Grill two minutes. Lower heat and cook 3-4 minutes on each side until reaching desired doneness.