Halve the honeydew melon and the water-melon and remove the seeds.
Using a melon-baller, scoop out the flesh and place in a bowl.
Slice the stem ginger and add to the melon with the ground cinnamon and port.
Cover and chill in the fridge for 3-4 hrs, stirring occasionally.
Transfer to a large serving dish, garnish with stem ginger, if using, and serve.