In a mixing bowl, combine the drained tuna, mayonnaise, Dijon mustard, diced celery, diced red onion, salt, and pepper. Mix well until fully combined.
Heat a frying pan or skillet over medium heat.
Take two slices of bread and spread a thin layer of butter on one side of each slice.
Place the buttered side down in the skillet, and spoon equal amounts of the tuna mixture on top of each slice.
Sprinkle shredded cheddar cheese on top of the tuna mixture.
Place another slice of bread on top of each sandwich, with the buttered side facing up.
Cook for about 4-5 minutes until the bottom side is golden brown and crispy. Carefully flip the sandwich with a spatula and cook the other side for an additional 4-5 minutes, or until golden brown and the cheese has melted.
Remove from the skillet and let it cool for a couple of minutes before slicing in half.
Serve hot and enjoy your delicious tuna melts!