Combine Gruyère cheese, Emmental cheese, and cornstarch in a bowl. Mix until the cheese is evenly coated. Set aside.
Rub the cut side of the garlic all over the inside of a fondue pot or heavy saucepan. Add wine and place over medium heat. Bring to a simmer, then gradually add cheese and cornstarch mixture. Stir with a spatula, gently stirring in a figure-of-eight motion, until all of the cheese is added and the fondue is smooth and homogenous. Reduce heat to medium-low if the fondue is boiling too vigorously.
Immediately serve fondue, preferably over a warmer. If you used a saucepan on the stove to heat the fondue, you can carefully transfer the fondue to a fondue pot to serve.
