1. Pour sugar onto a small, rimmed plate. Rub rims of two martini glasses with lemon wedge to moisten, then dip rims into sugar to coat (see notes).
2. Place ice in a cocktail shaker. Add vodka, liqueur, and lemon juice. Shake until mixture is very cold, about 10 seconds. Strain into glasses. Garnish each with a twist of lemon peel.