In a medium saucepan, combine the frozen or fresh blueberries, water, and granulated sugar. Stir gently to combine.
Place the saucepan over medium heat. Bring the mixture to a gentle boil while stirring occasionally. This will help the blueberries release their juices and the sugar dissolve.
Once the mixture is boiling, add the lemon juice or orange juice. This will add a bright, refreshing flavor that complements the sweetness of the blueberries.
In a small bowl, mix the cornstarch with 2 tablespoons of water to create a slurry. Once the blueberry mixture is bubbling, pour the slurry into the saucepan while stirring continuously. This will thicken the sauce, giving it that luscious consistency.
Continue to cook the sauce for an additional 2-3 minutes, until it has thickened to your liking. Keep in mind that it will thicken a bit more as it cools.
Remove the saucepan from the heat and let the sauce cool for a few minutes. If desired, you can strain it through a fine mesh strainer for a smoother texture. Serve your Homemade Blueberry Sauce warm or cool, depending on your preference.