In a 1 1/2- to 2-quart fondue pan (flame-proof ceramic or porcelain-glazed cast-iron) or heavy-bottom metal pan over medium heat, warm 1 cup wine until bubbles form and slowly rise to surface, about 6 minutes.
In a bowl, mix Swiss cheese, gruyère cheese, cornstarch, and mustard.
Add cheese mixture, a handful at a time, to hot wine, stirring until fondue is smoothly melted and beginning to bubble. Add kirsch and sprinkle fondue with nutmeg and pepper.
Set pan over an ignited alcohol or canned solid-fuel flame (if pan is ceramic, place a heat diffuser between it and heat source). Adjust heat so fondue bubbles very slowly. Check occasionally to be sure fondue is not scorching; if it is too hot, reduce or turn off the heat, then resume heating when mixture begins to cool.
Spear bread cubes, 1 at a time, with fondue forks or thin skewers (metal or wood) and swirl through fondue (stir across bottom frequently to prevent scorching); lift out and let drip briefly over pan, then eat. If fondue gets too thick for easy dipping, stir in more heated wine, a few tablespoons at a time. After fondue is consumed, scrape the cheese crust from pan to divide and eat; it's considered a special treat.