Cut a slice of lime, about 1/8-1/4 inch thick. Cut that slice into 4 wedges.

Pour about 1/4 cup super fine sugar onto a saucer slightly larger than your martini glass rim. Prepare your glasses by rubbing the rim of your glass with your lime wedge. Set wedge aside with the rest of your lime.

Place rim of glass in sugar and spin slowly to coat the rim. Cut watermelon slice about 1/4" thick from the center of the watermelon (cut slices for garnish). Set aside. Then cut the remaining watermelon into 1/4's and then in half and remove rind from watermelon.

Place a few pieces of the watermelon into a sieve, setting on top of a large bowl. Smash watermelon with a wooden spoon or a fork until fruit is sufficiently juiced. Pour juice into measuring cup, remaining watermelon into trash and repeat until you have 2 cups of watermelon juice. I used about 3/4 of a Dulcinea baby watermelon. Juice lime (including the wedges you cut for rimming the glasses) into sieve over bowl, pour juice lime into measuring cup.

Remove sieve and pour mixture back into bowl or into a martini pitcher. Add 1 cup of vodka to juice mixture (I recommend using a top shelf brand like Grey Goose or Absolut, as vodka is the only alcohol it is important to have a smooth one). Add ice cubes and stir. Remove ice cubes promptly once chilled.

Pour Watermelon Martini into sugar rimmed glasses. Garnish with watermelon slices and serve.