Chill your martini glass in the freezer before assembly.
Sprinkle sugar in a circle in a small dish.
Run a piece of the squeezed lemon along the rim of the glass and dip in the sugar.
Fill a cocktail shaker with ice and pour over it the Cognac, Cointreau, and lemon juice. Shake vigorously for 20 seconds.
Pour into the chilled glass.
Lay a strip of lemon peel on the rim and spear 2 maraschino cherries with a small skewer. Place inside the glass for garnish.