1. Combine 3/4 cup wine, lemon juice, and garlic in a medium heavy-bottomed saucepan over medium heat until bubbling. Reduce heat to low and gradually stir in cheeses, then continue to cook until cheeses melt, stirring frequently.
2. In a small bowl, blend cornstarch with remaining wine with a wire whisk until smooth. Stir into cheese mixture and continue to cook, stirring frequently, until mixture is thick, smooth and bubbling gently, 2 to 3 minutes more. Carefully transfer the mixture to a fondue pot, and keep warm over a fondue burner. Serve immediately with dipping ingredients of your choice.