Remove rind from orange in long strips with a sharp vegetable peeler, then juice the orange. You should have about 1/2 cup of juice. Transfer the rind and the juice to a small saucepan, and add the cranberries, ginger, rosemary, sugar, and water. Stir to combine, then bring to a boil over medium-high heat, stirring frequently. Lower the heat and gently simmer for 10 minutes, until the cranberries pop and release their juices. Remove from heat, and allow to cool to room temperature. Strain the cranberry mixture through a fine-mesh strainer, pressing down and scraping with a spatula to extract all of the juice. Discard the solids, and transfer to a jar. Store, tightly covered and refrigerated, for up to a week.

To serve, combine 3 parts syrup with 1 part lime juice. Pour over ice, top with sparkling water, and serve.