Puree the grapes in a blender, then strain the juices into a bowl. Season with balsamic vinegar if the grapes are too sweet. Combine the flour, cornmeal, salt, pepper, and rosemary on a plate, mixing well. Dip the tomato slices into the mixture, coating on both sides.
Pour a little olive oil into a large nonstick frying pan, just enough to create a film on the bottom. Add the garlic and place over medium heat. When the oil is hot, add the tomato slices and cook, turning once, until golden on both sides, about 6 minutes total. Sprinkle with salt and pepper, and using a spatula, transfer to a serving plate. Pour the grape juices over hot tomatoes. Serve at once.