Toss the cheeses with the flour in a bowl. Rub the inside of a saucepan with the cut sides of the garlic; discard the garlic.
Whisk the wine, lemon juice and mustard in the saucepan and bring to a gentle simmer over medium heat. Add half of the cheese mixture and stir with a wooden spoon until melted. Add the remaining cheese mixture and stir until smooth; add the nutmeg.
Continue to cook, stirring, 2 more minutes. Transfer to a fondue pot or slow cooker to keep warm. Serve with your choice of dippers.