In a small saucepan, combine pomegranate juice, sugar and rosemary. Bring to a boil and then reduce the heat to simmer.
Simmer for 15-20 minutes or until the syrup coats the back of a spoon. Remove from heat and let cool. Note: syrup will thicken as it cools.
Add 2 Tbsp pomegranate syrup to a champagne flute. Top with sparkling wine and pomegranate arils. Enjoy!