Combine sugar, water and cranberries in a small saucepan and bring to a boil over medium heat, stirring frequently. Reduce the heat to a simmer and continue to cook until the cranberries pop and soften and the mixture becomes thickens to a syrupy consistency (about 10 minutes)
Strain the cranberry syrup through a mesh sieve into a bowl. Use a spoon to press down on the cranberry mixture to release all the juice. Set syrup aside to cool to room temperature
Add two tablespoons of cranberry syrup to a glass and top with ½ teaspoon of fresh lime juice. Top with chilled prosecco.
Notes
The cranberry syrup will yield around ½ cup, or 8 tablespoons
The syrup can be made up to three days in advance and stored in an air-tight container in the refrigerator