Place the honeysuckle blooms in a large nonreactive bowl. Pour cold water over the blooms and stir a few times to mix. Allow the blooms to stand in the water for at least 24 hours, however for a more intense flavor you can allow them to stand for a few days.
Strain the mixture. Reserve the honeysuckle water and discard the blooms.
For the simple syrup, combine the remaining cold water and the sugar. Bring the water to a boil and simmer for 2 minutes until sugar is completely dissolved.
Stir in lemon juice and cinnamon. Allow simple syrup to cool.
If making sorbet, combine honeysuckle water and cooled simple syrup in the bowl of an ice cream maker and process according to manufacturer’s directions. Serve or freeze immediately.
If making granita, combine honeysuckle water and simple syrup and pour into a 9 x 12 x 2 inch glass baking dish. Carefully place the dish on a flat surface in the freezer. Freeze for two hours, then scrape the mixture with the tines of a fork. Return to the freezer. Repeat this process three more times, every two hours, for a total of eight hours.