Arrange the slices of prosciutto in a single layer on a baking sheet. Place in an oven heated to 350 degrees and bake for 12-15 minutes, until firm. Then remove from the oven the let cool.
While the prosciutto is in the oven, use a melon baller to create balls of honeydew and cantaloupe. If you don't have a melon baller, cut the melon into ½ inch cubes. Place in a serving bowl.
Finely chop the basil, and pour the basil and feta over the melon. Add the lime juice, and toss the ingredients to combine.
Lastly, crumble the prosciutto over the top and serve.