1. Light the grill or heat the broiler. Coat the tomato halves with 1 teaspoon of the oil. Grill the tomatoes cut-side up (or broil them cut-side down), until the skins start to blacken, about 10 minutes. Slip off the skins and put the tomatoes in a medium glass or stainless-steel bowl. Add the cucumber, lemon juice, dill, 3/4 teaspoon of the salt, and 1/4 teaspoon of the pepper. Stir to break up the tomatoes and to combine the ingredients.
2. Coat the swordfish with the remaining 2 teaspoons oil and sprinkle with the remaining 1/4 teaspoon salt and 1/4 teaspoon pepper. Grill or broil the fish for 4 minutes. Turn and cook until golden brown and just done, 4 to 5 minutes longer. Serve with the salsa.
Fish Alternatives: Halibut, marlin, and salmon steaks are also delicious grilled, and any of these would go well with the salsa.
Variations: Use 1 tablespoon chopped fresh basil in place of the dill. A tablespoon of fresh mint is another tasty alternative.
Wine Recommendation: A light white wine with plenty of refreshing acidity is perfect with both the fish and the fresh vegetables. Try a Muscadet de Sèvre-et-Maine from the Loire Valley in France.