1 1/2 tablespoons fresh ginger juice* (from one 3-ounce piece of ginger)
Ice cubes
Lime wedges
*To make ginger juice, peel a 3-ounce piece of ginger and grate it over a plate. Wrap in cheesecloth; twist at both ends to squeeze out the juice. Or put the grated ginger in a finemesh sieve and press to release the juices. In a pinch, bottled ginger juice is available at natural foods stores.
Directions
Place 2 1/2 cups watermelon and 3/4 cup cold water in blender. Puree until smooth. Pour agua fresca into large pitcher. Repeat 3 more times with remaining watermelon and cold water. Add lime juice, 1/4 cup sugar, and ginger juice to pitcher and stir to blend. Add more sugar by tablespoonfuls, if desired. Refrigerate until well chilled, at least 3 hours. DO AHEAD Can be made 8 hours ahead. Keep chilled. Stir before serving.
Fill glasses with ice cubes; pour agua fresca over. Garnish each glass with lime wedge and serve.