2 tablespoons Cointreau (or other orange liqueur), divided
2 tablespoons St-Germain liqueur, divided
1 bottle brut Champagne or Prosecco, well chilled, divided
In a small, heavy saucepan over high heat, boil pomegranate juice, sugar, and ginger until syrup is reduced to about 1/3 cup, stirring often, about 10 minutes. Strain and cool.
Pour 2 teaspoons pomegranate syrup, 2 teaspoons Cointreau. and 2 teaspoons St-Germain into each of four 6-ounce Champagne flutes. Fill each with sparkling wine.