Rinse and pat dry the swordfish steaks. Set aside.
Fish Marinade
Crush and chop the garlic. In a small bowl whisk together the melted butter, olive oil, garlic, zest of half the lemon and the juice.
Add rosemary to the melted butter mixture and pour over the swordfish in a plastic zip bag or container to marinate for 20 minutes or up to an hour tops. (See Note 1).
Broiled Swordfish
Preheat oven broiler. Place marinated swordfish on a rimmed baking sheet or oven safe grill pan.
Place under the broiler and cook fish for 2-3 minutes on first side, then use fish spatula to carefully flip swordfish steak over. Baste with additional marinade if desired and broil second side for 2-3 minutes. (See Note 2)
Grilling Option
Preheat grill to 500°F. Place swordfish on cleaned grill grates. Drop heat to 400°F and baste with reserved marinade.
Cook fish on first side for 2-3 minutes, use a fish spatula to gently flip it over, then grill the second side for 2-3 minutes. (See Note 2)
Video
Notes
Melted butter tends to solidify after 20 minutes in the refrigerator. Massage the bag of swordfish and marinade a bit to re-liquify the butter if necessary.
It's very easy for fish to over cook. To keep it moist, don't cook it for any longer than necessary.