The mint simple syrup can be made ahead and kept in a jar or other airtight container in the refrigerator for several weeks.
In a small saucepan, combine the sugar and water and bring them to a boil over medium heat. When the sugar is fully dissolved, boil for another 3 minutes. Remove the syrup from the heat and stir in the mint. Cover, and let the syrup steep for 30 minutes. Strain and discard the mint.
Serve the melon, cut however you like, with the syrup and a squeeze of lemon or lime juice, garnished with mint leaves.