Set a fine-mesh sieve over a small bowl; set aside.
In a small saucepan, boil ginger, sugar, and 1/4 cup water until it becomes a syrup, about 2 minutes. Remove from heat and pour through sieve and into a bowl, discarding solids.
Pour about a tablespoon of syrup into each champagne glass. Top with sparkling wine, gently stir.
To store syrup, refrigerate in an airtight container, up to 1 week.
Styling and Photography: Lisa Thiele / Recipe: Martha Stewart