Combine the canned tuna, celery, onion, mayonnaise, salt and pepper in a medium bowl. Stir to combine.
Place half of the tuna salad on one slice of bread and gently pat it down into an even layer. Top with two slices of Emmenthaler cheese and a second slice of bread. Butter both sides generously. Repeat to make a second sandwich.
Preheat a large skillet over medium heat. Add the sandwiches. Cook for two to three minutes until deeply golden, then flip. Toast the second side for two to three minutes, or until golden and the cheese is melted. Transfer the sandwiches to plates and enjoy warm.
