Gather your ingredients.
In a small bowl, mix together tuna, mayo, mustard, balsamic vinegar, relish, salt, and dill.
Pre-heat a griddle or frying pan on medium high.
Lightly butter one side of 2 slices of bread.
Place, butter side down, a slice of bread. Top with tuna mixture and a thick slice of Swiss cheese.
Top with remaining slice of bread. Grill on both sides until cheese is softened and bread is golden brown.
Remove sandwich from griddle and let rest 2 minutes. Slice on the diagonal and serve.