In a pitcher, combine the lime juice, pomegranate juice, Cointreau, tequila, and the sugar. Mix until the sugar has dissolved. Cover and refrigerate until chilled, about 1 hour.
Moisten the rims of the champagne glasses with the cut side of the lime. Spread coarse salt on a small plate, then upend the glasses into the salt to crust the rims. Fill each glass halfway with the margarita base (it'll take a generous 1/3 cup). Slowly fill the rest of the way with champagne or sparkling wine, and hand to one of your lucky guests.