In a bowl, mix together the tuna, mayo, mustard, and celery or onion. Season with salt and pepper to taste.
Butter one side of each slice of bread.
Heat a skillet over medium heat. Place two slices of bread butter-side down in the pan.
Spread tuna salad on each slice, top with a slice of each kind of cheese, and place the remaining bread slices on top, butter-side up.
Grill for 2–3 minutes per side, pressing lightly with a spatula, until the bread is golden and the cheese is melted.
Slice and serve hot.