In a pitcher, stir together the lime juice, sugar and 1 cup water until the sugar has dissolved. Add the grapefruit juice and stir to combine. Cover and refrigerate until chilled, about 1 hour.
Add the tequila and 1/2 teaspoon salt to the pitcher to finish the base. Moisten the rims of the glasses with the cut side of the lime. Spread coarse salt on a small plate, then upend the glasses into the salt to crust the rims. Fill the glasses 3/4 full with ice and add 6 ounces of the tequila mixture to each. Top off each cocktail with 1 ounce sparkling water, stir to combine and enjoy.