Thaw cherries if frozen; do not drain. In a blender or food processor combine cherries and 1 cup of the water. Cover and blend or process until pureed. Press cherry mixture through a fine-mesh sieve; discard pulp.

In a large bowl combine strained cherry mixture, remaining water, sugar, fruit juice or champagne, and lemon peel, stirring until sugar dissolves. Pour into a 2-quart square baking dish. Cover and freeze 5 to 6 hours or until almost firm. Break the frozen mixture into chunks.

Transfer chunks to a large, chilled mixing bowl. Beat with an electric mixer on medium speed until smooth but not melted. Return quickly to the cold dish. Cover and freeze for 6 to 8 hours more or until sorbet is firm. Use an ice cream scoop or large spoon to serve into dishes.

If using a food processor, puree the cherries half at a time.

Freeze for up to 2 weeks.