Place the pomegranate juice, rum, orange liqueur and lime juice in a blender. Add ice cubes. Pulse and blend until ice cubes are finely crushed. Divide the daiquiri mixture between four large, chilled martini or other decorative glasses. Set a few pomegranate seeds in each glass. Garnish the rim of each glass with lime slice and mint sprig and serve.
Make cranberry daiquiris by replacing the pomegranate juice with cranberry juice. And, instead pomegranate seeds, garnish each drink with a few dried cranberries.
Or, make pomegranate cranberry daiquiris by using a mix of those two juices; garnish with pomegranate seeds or dried cranberries, or a mix of the two.