Rub the lime wedge around the rim of each martini glass. Place the lime salt on a small plate and dip the rim of each glass into the salt, coating it evenly. Set the glasses aside.

Place the watermelon chunks in a blender and blend until smooth. Strain the watermelon juice through a fine mesh strainer into a bowl or directly into your cocktail shaker to remove any pulp.

In the cocktail shaker, combine the strained watermelon juice, premium vodka, and freshly squeezed lime juice. Fill the shaker with ice, secure the lid, and shake vigorously for about 15 seconds until well chilled.

Strain the mixture into the prepared martini glasses. If desired, garnish each glass with a small watermelon cube on the rim or skewered on a cocktail pick. Serve immediately and enjoy!