Place squash, cut sides down, in a microwave-safe 2-quart rectangular baking dish; add the water. Prick skin all over with a fork. Cover with vented plastic wrap. Microwave on 100 percent power (high) about 10 minutes or until squash is tender. Let squash stand for 5 minutes.
Combine oil, Italian seasoning, salt, and pepper. Using fork, remove pulp from squash shells, separating it into strands. Transfer to bowl; toss with 2 teaspoons of the oil mixture and the Parmesan cheese. Fold a 36x18-inch piece of heavy foil in half to make a double thickness of foil that measures 18x18 inches. Place squash mixture in center of foil. Bring up opposite edges of foil and seal with double fold. Fold remaining edges to completely enclose the squash mixture, leaving space for steam to build. Grill squash packet on the rack of an uncovered grill directly over medium heat for 10 minutes, turning once. Toss tomatoes with remaining oil mixture. For last 5 minutes of grilling, place tomatoes on grill rack beside packet. Grill tomatoes just until tender, turning once. Transfer tomatoes to cutting board; cool slightly and chop. Spoon over squash; sprinkle with basil. Makes 4 to 6 servings.