Put oven rack in middle position and preheat oven to 250°F.

Toss tomatoes with sugar, 1/2 teaspoon salt, and 1/4 teaspoon pepper and arrange, cut sides down, in a small shallow baking pan. Heat oil in a 9- to 10-inch heavy skillet over moderate heat until hot but not smoking, then cook garlic, stirring occasionally, until pale golden, 1 to 2 minutes. Stir in basil and whole oregano leaves, then pour oil over tomatoes. Roast tomatoes until very tender but not falling apart, 2 1/4 to 2 1/2 hours.

Transfer tomatoes with a spatula to a large plate, then pour oil through a fine-mesh sieve into a small bowl or measuring cup, discarding solids. Stir in chopped oregano, zest, juice, and remaining 1/4 teaspoon salt and pepper.

Combine lemon juice, white wine, olive oil and some salt and pepper in a shallow pan. Add in the fish fillets and marinate 15 minutes to 1/2 hour. Light a barbecue and cook the Mahi Mahi, about 6 minutes on each side. Serve on a plate and drizzle over the Lemon Oregano oil, sprinkle with olives and cilantro, and place two tomatoes on the side of each fish.