In a food processor, purée the honeydew, the mint leaves, the lime juice, the sugar to taste, and a pinch of salt until the mixture is smooth. Transfer the soup to a large bowl or wide-mouth jar, cover tightly, and chill for at least 1 hour or overnight. The soup may be made 2 days in advance and kept in the refrigerator, tightly covered.
If you are using the cantaloupes, decoratively halve them, remove the seeds, cut a small slice from the bottom to allow them to sit firmly on a plate, and chill before serving. Ladle the soup into the cantaloupe halves or bowls, and optionally garnish with additional mint leaves.
Serves 8-12 depending on whether you use the cantaloupes to serve the soup.