1. Spray the grill rack with nonstick spray; prepare the grill for medium-hot fire.
2. Combine the garlic, basil, salt, and oil in a small bowl.
3. Spoon the herb mixture onto the cut sides of the tomatoes and let stand at room temperature 1 hour. If using plum tomatoes, thread them on skewers.
4. Grill the tomatoes 5 inches from heat, at edge of grill, turning once, until hot, about 10 minutes for medium tomatoes, and 5 minutes for plum tomatoes. Serve the tomatoes hot, or at room temperature.