Add the blueberries to a blender or food processor and process until smooth. Push the mixture through a fine wire strainer into a small saucepan.
Add the sugar to the saucepan and stir until dissolved. Heat the blueberry mixture over medium heat until it just reaches a simmer. Remove from heat and let cool.
When ready to serve, pour 2-3 tablespoons of blueberry syrup into a glass. Squeeze a lime wedge over the syrup. Add a few scoops of ice cream, then pour the sparkling water over the top. Serve immediately.