Place swordfish steaks in a shallow dish, rub with olive oil and sprinkle with salt and pepper.
Combine light rum, lime juice, chopped mint, and garlic in a small bowl.
Pour marinade over the top of the swordfish steaks.
Put in refrigerator and let marinate for about 20 minutes, but be sure not to let it sit much longer or the lime juice may cook the fish.
Heat grill to medium-high heat and brush grates with canola oil.
Place swordfish steaks on grill and cook for about 3 minutes on each side, depending on thickness, until swordfish is cooked through.
Sprinkle with additional mint and serve with lime wedges.