Cut the zucchini and yellow squash in half crosswise, then cut each into ¼-inch lengthwise slices.
In a large bowl, toss the zucchini, yellow squash and red bell pepper with olive oil, balsamic vinegar, salt and pepper.
Place the vegetables on the grill and cook until tender, about 2 minutes for side for the zucchini and squash, and 3 minutes per side for the red bell pepper.
Preheat a panini press.
Spread 1 tablespoon of the tomoato sauce on each cut side of the ciabatta rolls.
Divide the zucchini, yellow squash and red bell pepper pieces evenly between the 4 rolls. Top with fresh mozzarella and basil, and close the sandwiches.
Place the sandwiches on the panini press (this may need to be done in two batches). Alternatively, you can lay a heavy pan or foil-covered brick on the sandwiches, on the grill.
Grill until the bread is toasted and the cheese is melted. Cut the sandwiches in half and serve.