To make watermelon juice, scoop half a small watermelon into a blender and puree until well blended. Then strain through a fine mesh strainer and place juice in a jar. Refrigerate until ready for use.
To make watermelon ice cubes, cube the other half of the watermelon into ice cube-sized pieces and place on a baking sheet. Make sure they're not touching of they'll stick together. Freeze for 4-5 hours or overnight or until very firm.
To make margaritas, add watermelon juice, lime juice, tequila, and triple sec to a cocktail shaker or pitcher and shake vigorously or stir.
Next, run the quarter of a lime around two serving glasses and then dip in margarita salt. Fill 3/4 of the way full with watermelon ice cubes (or regular ice cubes if preferred).
Divide the margarita between glasses (2 as original recipe is written) and serve immediately. Garnish with an additional lime wedge.