Using a vegetable peeler, remove the zest from the limes in long strips. Cut the zest into fine, needle-thin julienne, reserve.

Section the limes and remove the pith and membrane, reserve 4.

In a medium saucepan, combine the sugar with 1 cup of water and bring to a boil over high heat. Continue boiling for 5 minutes and remove from the heat. Fold in the lime zest julienne and let steep for 2 minutes. Remove the zest with a slotted spoon to a sheet of waxed paper. Add the tequila to the syrup.

Halve and seed the melons. Cut into long 1-inch-wide-strips. Remove the melon rind with a sharp paring knife.

Arrange the melon slices attractively on a platter or serving dish. Sprinkle the lime sections and the lime julienne over the melon. Pour the syrup over the fruits and serve with the mint.