Hi Mary, Yes, you can freeze blueberry syrup – and most syrups will keep in the fridge for up to a week.  You can easily freeze the syrup in a covered plastic container.  In addition, a favorite trick of mine is to freeze  syrup (and sauces, and stock) in ice cube trays. Then, once frozen, transfer the cubes to a heavy-duty zipper plastic bag. That way, you’ll have serving-size portions that you can defrost individually.