In a small saucepan, heat pomegranate juice to near boiling, add cinnamon stick, and simmer for 10 minutes. Remove from heat and allow to cool completely, at least 1 hour. Remove cinnamon stick. Divide the spiced juice between 2 tall glasses; add 1 cup sparkling mineral water to each glass. Stir, add ice, and serve with a garnish of frozen cranberries.