In two batches, pulse the watermelon cubes in a blender just until it looks like a chunky sauce, about 10 to 12 short pulses. Transfer pulp to a colander lined with cheesecloth set over a large pot, stirring occasionally until most of the liquid has dripped through. Transfer 3 ½ cups of liquid to a large pitcher and reserve remainder for another use.
Add lime juice and agave nectar to pitcher and stir to combine. Refrigerate until completely cool. Serve in ice-filled glasses, garnished with lime zest or rings if desired.
