In a medium mixing bowl, stir together the tuna, mayonnaise, tarragon, lemon juice, salt, and pepper.
Spread one side of each of the pieces of bread with a portion of the butter.
In a large non-stick skillet over medium high heat, place 4 of the slices of buttered bread, buttered side down. Top each piece with ¼ of the tuna mixture.
Top each tuna mixture with a slice of tomato, then with a slice of cheese.
Finish each sandwich with another piece of bread, buttered side up. Cook for about 3 minutes, until the underside of the bottom bread begins to brown. Turn the sandwiches over and continue cooking until the underside is browned and the cheese has melted.