Preheat barbecue to medium-high. In a small bowl, whisk balsamic vinegar with olive oil. Lightly brush cut tomato sides with a little vinegar mixture.
Grill cut-side down, until slightly tender, 3 to 5 min. Baste with vinegar mixture, turn and grill for 2 min. more. In a bowl, toss croutons with basil. Plate tomatoes cut-side up, drizzle with remaining vinegar mixture and sprinkle with salt and pepper and crouton mixture. Serve immediately.