Place zucchini and squash in square baking dish 8 × 8 × 2 inches. Mix remaining ingredients; pour over vegetables. Cover and let stand at least 1 hour but no longer than 2 hours.
Heat coals or gas grill. Remove vegetables from marinade; reserve marinade. Cover and grill vegetables 4 inches from medium heat 10 to 15 minutes, turning and brushing 2 or 3 times with marinade, until golden brown and tender.
Cut each crosswise into 4 pieces. Toss with any remaining marinade.