Rub the inside (bottom and sides) of a cheese fondue pot with the garlic clove; discard the garlic.
Combine the wine, flour or cornstarch, and lemon juice in the fondue pot and cook over medium-low heat, stirring occasionally, until bubbling, 1-2 minutes.
Gradually add the shredded Swiss and Gruyère cheeses, about 1/2 cup at a time, stirring constantly with wooden spoon over low heat, until cheeses are melted. Stir in kirsch or sherry.
Keep warm over simmer setting or transfer to a double boiler. Spear Party Potato Rolls and other accompaniments with fondue forks or skewers; dip in the fondue, and enjoy or make into mini sandwiches.
Tip: If fondue becomes too thick, stir in 1/4 to 1/2 cup heated wine.