Heat a grill to medium.
Spread 2 tablespoons sauce on each cut side of each ciabatta half. Put half of the basil leaves on the ciabatta bottoms and top with the mozzarella, then the tomato and remaining basil. Sandwich with the top halves.
Place on the grill and put a skillet on top. Cover and grill until grill marks appear on the bottoms, about 3 minutes. Carefully remove the skillet and flip over the sandwiches. Replace the skillet, cover, and grill until grill marks appear, about 3 minutes. Carefully remove the skillet and transfer the sandwiches to serving plates.
You can substitute focaccia for the ciabatta. You can grill these in a grill pan or heavy skillet.