Combine ice, Cointreau, lime juice, tequila, champagne, and sugar in a blender and pulse until slushy. Run a lime wedge along the edge of the margarita glasses then upend the glass in sugar or salt to line the rim. Pour margaritas into glasses and garnish with a lime wedge.
Notes
Cointreau can be substituted for triple sec or left out entirely to let the tequila shine.