Combine the sugar, water and cranberries in a small saucepan. Cook over medium heat until simmering. Stir occasionally. Continue to cook about 10 minutes until cranberries have popped and the mixture has become syrup like.
½ Cup Cranberries, ½ Cup Sugar, ½ Cup Water
Remove cranberries from heat. Strain through a mesh sieve, pressing the cranberries with a spatula to get all of the juice. Let syrup cool to room temperature.
Place 2 tablespoon of cranberry syrup and ½ teaspoon of lime juice into a glass. Top with chilled prosecco.