Place the melon chunks in a plastic bag, and freeze until solid.
Run the lime wedge around the rim of a large stemmed cocktail glass. Dip the moistened rim in salt. Set the lime wedge and glass aside. Repeat with the remaining wedges and 3 more glasses.
Transfer about 3/4 of the melon chunks, separating them, to a blender. Add the tequila, triple sec, and lime juice, and blend until fairly smooth. Divide the cocktail mixture among the prepared glasses. Squeeze a lime wedge into each cocktail, drop the wedge into the glass and serve immediately.
For an extra touch of color and flavor, mix 2 teaspoons finely minced lime zest (colored peel) into the salt before rimming the glass.