1. Combine first 5 ingredients in a large bowl.
2. Place mixture on cooking grate, and grill, covered with grill lid, over medium-high heat (350° to 400°). Grill tomatoes 3 minutes or just until they begin to pop. Turn okra, and grill, covered with grill lid, 2 to 3 more minutes or until tender.
3. Transfer okra and tomatoes to a serving dish, and sprinkle with basil. Serve immediately.