Place 4 glasses in the freezer to chill. Before serving, rub the inside of each glass with a lime wedge. For each drink, pour 1/3 cup gin, 1/2 cup tonic water, and 1 cup ice cubes in a martini shaker. Shake once or twice. Strain into a glass just until the liquid is about 2 inches below the brim (do not overfill). Top each cocktail with 1/4 cup Champagne. Serve immediately with skewered lime wedges.