Place cranberry juice in a medium saucepan and bring to the boil over high heat. Cook, uncovered, for 10 minutes or until reduced by two-thirds. Remove from heat and set aside for 30 minutes to cool.
Combine the cranberry juice, Cointreau and lime juice in a small jug. Place a sugar cube in each serving glass. Pour the cranberry mixture over the sugar. Top with Champagne or sparkling wine and serve immediately.