In batches, puree watermelon cubes in a blender until smooth. Pour through a fine-mesh sieve into a liquid measuring cup, pressing on solids to extract liquid; discard solids. Add liquid back to blender. Add vodka, liqueur, lime juice and ice; blend well.
To rim the martini glass with sugar or salt: Smooth out a thick layer of sugar or salt onto a surface wider than your glass. Go around the rim with a bit of lime juice. Press the top of the glass into the sugar or salt and gently rotate until coated.
Fill each martini glass and garnish with slices of your choice citrus.
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