1. Bring first 3 ingredients to a boil in a small saucepan, stirring just until sugar dissolves. Cover and remove from heat; let stand for 20 minutes. Strain through a fine sieve over a bowl, reserving liquid; discard solids. Cover and chill.
2. Combine chilled syrup, vodka, and juice. Pour over ice in a martini shaker; shake to combine. Strain into 6 martini glasses; garnish with rosemary, if desired.