In a large microwave-safe bowl, whisk together pomegranate juice, pineapple juice, and sugar until sugar is dissolved. Microwave on high for 15 seconds.

Pour mixture into an ice cream maker, and process according to manufacturer’s instructions.

Place in an airtight container, and freeze until solid, at least 4 hours. Keeps for up to 2 weeks. Serve with pineapple wedges, if desired.