Combine sugar and 1/4 cup water in a small saucepan; bring to a boil. Reduce heat, and simmer 2 minutes or just until sugar dissolves. Remove from heat; cool.
Combine sugar syrup, club soda, pomegranate juice, vodka, and lime juice. Place crushed ice in a martini shaker; add about 3/4 cup pomegranate mixture. Cover and shake. Strain into a glass. Garnish with lime slice, if desired. Repeat procedure with remaining pomegranate mixture.
Key limes are smaller, rounder, and more robustly flavored than the common Persian lime and often have yellow-green skin. They're perfect for this drink, but you can substitute 1/4 cup regular lime juice. Prepare the syrup a day ahead, and keep it in the fridge until you're ready to mix the cocktails. For a festive touch, sugar the rims of the glasses.