1. Rub rims of 8 (8-ounce) martini glasses with 8 grapefruit wedges.
2. Place sea salt into a shallow dish and dip martini-glass rims in the salt.
3. Fill martini shaker halfway with crushed ice. Add 1/2 cup vodka and 3/4 cup grapefruit juice; shake to chill.
4. Strain evenly into 4 of the martini glasses. Stir in 2 tablespoons club soda per glass. Repeat to make 8 drinks.
5. Garnish glasses with grapefruit wedges.