Place the ice in a punch bowl. Add the simple syrup, pomegranate juice, and cranberry juice. Stir well. Slowly pour in the sparkling water. Garnish with lime slices, mint sprigs and pomegranate seeds, if using, and serve.
For the simple syrup:
In a saucepan, combine water and sugar over medium heat. Bring to a boil, reduce heat and simmer for 5 minutes, stirring occasionally, until the sugar has dissolved. Take the pan off the heat and allow the syrup to cool.
Serving Suggestion: As an alternative to serving from a punch bowl, make the bellini mixture in a 1.4 to 1.8L capacity pitcher. Divide the pomegranate seeds between 12 champagne flutes. Add 1 slice of lime and 1 sprig of mint to each glass. Pour the bellini mixture into the prepared glasses and serve.