Prepare the tuna salad by mixing canned tuna with mayonnaise, chopped celery, diced onion, salt, and pepper in a mixing bowl. Adjust seasoning to taste.
Lay out four slices of bread, spread a generous amount of tuna salad on each, top with cheddar cheese and tomato slices, and add more salt and pepper if desired. Place another slice of bread on top.
Spread softened butter on the outside of each sandwich.
Preheat your skillet over medium heat and place the sandwiches in the skillet, working in batches if necessary.
Cook each sandwich for about 3-4 minutes on one side until golden brown, then flip and cook for another 3-4 minutes. Cover with a lid if cheese isn't melting.
Remove sandwiches from the skillet once golden brown and cheese is melted. Cut in half and serve warm.