Bring wine and lemon juice to a low boil in a heavy saucepan; add cheeses, pepper, and nutmeg, if desired. Reduce heat to medium-low, and cook, stirring constantly, 5 to 7 minutes or until cheese melts.
Whisk together cornstarch and cherry brandy. Stir mixture into cheese; cook, stirring constantly, 3 minutes or until thickened. Transfer to a fondue pot, and keep warm. Serve with cubed bread or steamed vegetables.