Thaw fish, if frozen. Rinse fish and pat dry with paper towels. Measure thickness of fish.

For red pepper sauce: In a small skillet, heat 1 tablespoon oil over medium heat. Add sweet pepper; cook for 3 to 5 minutes or until tender, stirring occasionally. Stir in tomatoes, 1 tablespoon of the vinegar, the salt, and cayenne pepper. Cook about 5 minutes or until tomatoes soften, stirring occasionally. Cool slightly. Transfer mixture to a blender or food processor. Cover and blend or process until smooth. Return sauce to skillet; keep warm over low heat.

In a small bowl, stir together the remaining 1 tablespoon vinegar, 1 tablespoon oil, and the snipped or dried basil; brush onto the snapper fillets.

Place fish on the lightly greased rack of an uncovered grill directly over medium coals. Grill for 4 to 6 minutes per 1/2-inch thickness of fish or until fish flakes easily when tested with a fork, turning once halfway through grilling.

Serve fish with red pepper sauce. If desired, garnish with cherry tomatoes and fresh basil sprigs. Makes 4 (1 fillet and 1/4 cup sauce) servings.