1. In a bowl, combine the cheeses, caraway and cornstarch.
2. Rub garlic around the inside of flameproof fondue pot or large saucepan. Discard garlic. Add beer and lime juice and bring to a simmer over medium heat.
3. Reduce heat to medium-low. Add cheese, a handful at a time, stirring constantly in a figure-eight motion with a wooden spoon until cheese is melted.
4. Remove from heat and set up on a fondue stand with a burner if desired. Serve with bread or other dippers.
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