Place watermelon cubes in the jar of a blender. Process until smooth.
Strain watermelon puree through a fine mesh sieve, pushing pulp against sieve with a spatula or back of a large spoon to extract as much juice as possible. Discard pulp.
Stir in salt, if desired, and refrigerate if not using immediately. Makes approximately 3 cups of watermelon juice. Drink it plain, as the base for mocktails (see ideas below) or use it to make 8 watermelon margaritas.
Rim margarita glass:
Place a small amount of kosher salt on a shallow plate.
Run a lime wedge around the rim of the glass.
Dip the rim in the salt, rotating the glass as needed to cover the entire rim.
To make one margarita:
Fill cocktail shaker and prepared glass with ice.
Add all ingredients to the cocktail shaker (except simple syrup if you have a very sweet melon), cover and shake vigorously for at least 20 seconds.