Heat wine, stock, kirshwasser and garlic to a simmer. Once brought to a simmer, allow to simmer for 5 minutes.
Mix Gruyere cheese, Swiss cheese and cornstarch together.
Reduce heat to low and using a wooden spoon, sprinkle some of cheese mixture into liquid and continue to stir in small amounts of mixture until all cheese is incorporated and fondue is smooth and melted.
Keep warm and serve warm.