In the food processor, blend melon, sugar, lemon juice and port, if desired, until smooth. Add more sugar if needed. Freeze granita using one of the methods described below.
Divide prosciutto among serving dishes. Spoon granita into dishes and serve immediately.
Classic Granita Method:
Pour the granita mixture into a wide and shallow container, such as a stainless steel baking dish (the shallower the container, the quicker the granita will freeze).
Cover with a lid, foil or plastic wrap. Freeze the mixture 1 to 2 hours, until it is solid around the edges. Take the container out of the freezer and scrape the ice with a fork, mixing it from the edges into the center.
Repeat this scraping and mixing process every 30 minutes or so (at least three times) until the entire mixture has turned into small, sequined ice flakes. When ready to serve, "rake" with a fork to loosen the granita and spoon into serving dishes.
Quick Granita Method:
Note: This method is faster, but the granita will have a different texture—less icy and more slushy.
Pour the granita mixture into ice trays, cover with plastic wrap, and allow to freeze solid. Process the cubes in a food processor when you're ready to serve.