Combine all ingredients in a small saucepan and bring to a simmer over medium-low heat. Simmer 10 minutes.
Remove from the heat and cool completely.
Strain the syrup into a glass container and store in the refrigerator up to 2 weeks. Makes about 2 cups syrup, enough for 16 drinks or to serve by the pitcher.
To mix one drink:
Add some ice cubes to a glass.
Add the Campari and ginger syrup. Pour in enough hard cider to fill the glass by 2/3. Stir with a spoon to combine.
Add about a tablespoon of pomegranate seeds to the glass, then top off with the sparkling wine.
To make a party batch of drinks, multiply the syrup, cider and Campari by the number of desired servings and combine in a pitcher. Pour the mix over ice when ready to serve, then top off with the sparkling wine.
The ginger syrup keeps in the refrigerator for a couple weeks — try adding it to plain sparkling water for a delicious flavored soda.