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For the Salsa: Simply combine the chopped tomatoes, oil, both kinds of olives, basil, parsley, capers, and vinegar in a nonreactive bowl. Season to taste with salt and pepper. Make this at least an hour before cooking the fish.
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For the Fish: Whisk the oil, lemon juice, basil and salt together in a large, broad bottomed non-reactive bowl and season generously with black pepper. Add the fish, turning the pieces over the coat and allow to marinate for about 10 minutes, while grill preheats.
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Meanwhile, prepare a hot fire over hardwood charcoal, or set gas grill to high; alternatively heat a grill pan over high heat on the stove (we like cast iron). Make sure grates or ridges are clean and brush them lightly with vegetable oil. Lift swordfish out of marinade allowing excess to drip away; discard marinade.
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Grill swordfish for about 3 to 4 minutes per side. The fish should take on a little color in addition to grill marks and you can check the insides with the tip of a sharp knife; the flesh should be opaque and your knife should meet little resistance. Serve immediately with salsa spooned over the top. Rice makes a great accompaniment.