If using tangerines, use a vegetable peeler or a thin sharp knife to thinly peel the tangerines (refrigerate fruit for another use). Trim peel to form about 6-inch-long spirals. Place a tangerine spiral in each chilled champagne glass, or set spirals aside to add to the rims. If desired, place 1 or 2 maraschino cherries in each glass.
In a glass pitcher, combine cranberry juice, Triple Sec, and maraschino cherry juice.
For each serving, pour about 1/4 cup cranberry juice mixture into each champagne glass. Add about 1/4 cup champagne, filling glass nearly to the top. Gently stir with an up-and-down motion to mix the drink without destroying the carbonation of the champagne. Makes 12 to 14 (4-ounce) servings.