Add the cheeses and cornstarch to a medium-size bowl. Using clean hands, toss the cheese with cornstarch to combine.
Add the wine, lemon juice, mustard, garlic powder and a pinch of nutmeg to a fondue pot or a heavy bottom ceramic saucepan. Whisk to combine and bring to a simmer over medium-low heat. Gradually add the cheeses in cup-size increments, being sure to let the cheese completely melt before adding more. Avoid over-stirring, as it could make the fondue stringy. Add salt to taste.
Keep warm in a fondue pot and serve immediately. Use fondue forks or wooden skewers to dip dippers into fondue.