In a medium saucepan, combine the frozen or fresh blueberries, water, and granulated sugar. Stir gently to mix.
Place the saucepan over medium heat. Cook the mixture, stirring occasionally, until the blueberries start to burst and release their juices, about 5 to 7 minutes.
Once the blueberries are bubbling, add the lemon or orange juice. This will enhance the flavor of the sauce and give it a refreshing zing.
In a small bowl, mix the cornstarch with 2 tablespoons of water until smooth. Gradually add this mixture to the blueberry sauce while stirring continuously. Continue to cook for 1-2 minutes until the sauce thickens to your desired consistency.
Remove the saucepan from heat and let the sauce cool slightly. It will thicken more as it cools. Transfer the sauce to a jar or container and let it cool completely before storing it in the refrigerator.
