Thaw shrimp, if frozen. Peel and devein shrimp, keeping tails intact. Rinse shrimp; pat dry with paper towels. Set aside.
In a small food processor bowl or a blender container combiner tomato, tarragon, lemon juice, garlic, salt, and pepper. Cover and process or blend with several on/off turns until mixture is coarsely chopped. Remove half of mixture (about 1/3 cup) to a small bowl and set aside. Process or blend remaining mixture until nearly smooth.
In a large plastic bag combine shrimp and the smooth tomato mixture. Seal bag. Marinate in refrigerator for 30 to 45 minutes. On 2 long metal skewers, thread shrimp, leaving a space of about 1/4 inch between pieces to allow for even cooking. Grill on rack of an uncovered grill directly over medium coals for 8 to 10 minutes or until shrimp are opaque, turning once. Remove shrimp from skewers and place them in a bowl. Toss shrimp with the reserved, coarsely chopped tomato mixture. Serve in individual cocktail glasses. Makes 4 appetizer servings.