In a bowl, add drained tuna, mayonnaise, and pickle relish. Mix with a fork. Blend well.
Spread the outside of each sandwich thin with ½ teaspoon butter. Spread the inside of each slice with mustard.
Divide the tuna and spread over each sandwich thin bottom, on the mustard side. Top each with 1 slice tomato. Sprinkle each with 2 tablespoons cheese. Place the remaining slices (mustard inside) on top to create a sandwich.
In a large nonstick pan, add the two sandwiches, cheese side up. Cover the pan with a lid and cook on medium-high heat for about 2-3 minutes, until the bottom is golden brown. Using a spatula, turn each sandwich over. Flatten a little with the spatula. Cover and cook another 1-2 minutes until golden. Turn sandwiches over again and cook, uncovered about 30 seconds more, until cheese is melted.
Serve at once.