In a large bowl, combine chopped chicken breast, celery, mayo, mustard, relish, salt, and pepper until well mixed.
Preheat a large, heavy bottom skillet over medium heat.
While the skillet heats, assemble your sandwiches. On a cutting board, place 2 slices of bread next to each other. Stack each piece of bread with 2 slices of cheese, 1 slice of tomato and half of your chicken mixture. Top with the remaining 2 slices of bread.
Spread butter over the outside of the sandwich bread on both sides and set into the skillet, butter side down, for about 4 minutes until the bread is brown and toasted.
Flip and cook on the other buttered side pressing down with a flat spatula to ensure good contact with the skillet. Cook until bread is golden brown and crisp and cheese is melted, about 4 minutes per side. Serve warm.