After cubing your watermelon and cucumber, place in food processor or blender and puree.
Pour puree into a sieve over a large bowl, pressing down on the solids with a spatula to get out all the juice.
In a small bowl, mix together the lime juice and agave nectar or honey. Then add to the watermelon and cucumber juice. Taste and adjust sweetness to your liking with more agave nectar or honey if necessary.
To serve, place two basil leaves at the bottom of a glass and bruise with muddler or anything available, to release the basil herbal scent.
Add ice and then pour the juice mixture into the glass. Add a cucumber slice or two on top and another piece of basil.