In a blender, puree the watermelon until smooth. If you prefer a thinner liquid, set a fine-mesh strainer over a bowl and strain the watermelon juice, pressing gently on the solids to extract as much juice as possible. Discard the pulp.

In a large pitcher, combine the lime juice, watermelon juice, St. Germain and tequila. Refrigerate until chilled, about 2 hours.

Pour the cocktail into tall ice-filled glasses. Garnish with the watermelon and/or lime wedges and serve.