In a small saucepan, combine the water, sugar and ginger and bring to a boil. Cover and simmer over low heat for 10 minutes. Strain the ginger syrup into a small bowl.
Puree the cubed watermelon in a food processor. Strain the puree through a fine sieve set over a bowl. Stir in the ginger syrup and the lime juice.
Fill 8 tall glasses with ice and add the limeade. Garnish with the melon wedges and serve.