Place the watermelon (with seeds removed) and cucumber in a blender and process until pureed. Pour through a fine mesh strainer or fine-mesh sieve to remove any excess pulp.
Set out two glasses and fill each with ice. Pour 1 1/2 ounces of gin into each glass, then divide the watermelon-cucumber mixture between the two cocktails. Stir well and serve immediately.
Notes
To store, put in the refrigerator for up to 24 hours in a covered container. To maintain its refreshing quality. If you need to prepare it in advance, blend the ingredients and chill the mixture, adding ice and gin just before serving to keep it fresh and vibrant.