Peel the kiwi fruit, cutting out the hard stem. Cut the pulp into small cubes. Spread the fruit cubes on a plate and drizzle with lime juice. Place the plate in the freezer for an hour.
In the meantime, bring the sugar to the boil with 125 ml of water until the sugar has dissolved and a syrup has formed. Let the sugar syrup cool down. Puree the frozen kiwi cubes with the sugar syrup in a blender or hand blender. Freeze the mixture in an ice cream maker.
Fill the finished sorbet into a piping bag with a star nozzle. Pour the sorbet decoratively into glasses and add a little champagne or sparkling wine if you like.
Put the rest of the sorbet in the piping bag in the freezer, consume gradually.