In a medium bowl, combine the drained tuna, mayonnaise, sweet pickle relish, Dijon mustard, black pepper, and salt. Mix well until all ingredients are evenly incorporated.
Spread the softened butter evenly on one side of each slice of bread.
Place two slices of bread, buttered side down, on a clean work surface.
Divide the tuna mixture evenly over the unbuttered sides of the two bread slices.
Top each with two slices of cheddar cheese.
Place the remaining two slices of bread on top, buttered side up, to form sandwiches.
Heat a large skillet over medium heat.
Place the sandwiches in the skillet and cook for about 4-5 minutes on each side, or until the bread is golden brown and the cheese has melted.
Remove the sandwiches from the skillet and let them cool for a minute before slicing in half and serving.