To make the watermelon juice, put the watermelon cubes into a blender. Blend until smooth. Strain through a fine-mesh sieve, pressing on solids.
If not using immediately, store in an airtight container or pitcher in the refrigerator for 3-4 days.
Chill a martini glass in the freezer for 15-20 minutes.
Mix Martini
Add watermelon juice, vodka, orange liqueur, lime juice and simple syrup into a cocktail shaker. Fill it with ice and shake vigorously for 15 to 20 seconds, or until the shaker feels very cold.
Strain into chilled martini glass. Garnish and serve.
To Make Simple Syrup
In a small saucepan over medium heat, combine the water and sugar, stirring until the sugar is completely dissolved, about 2 minutes
Cool, then transfer the mixture to a small container and store in the refrigerator for up to a month.
Notes
Use cold watermelon: Starting with chilled watermelon helps the cocktail taste colder and fresher.
Strain the juice: This keeps the martini smooth and elegant instead of pulpy.
Adjust the sweetness: Watermelons vary a lot. Start with ½ ounce simple syrup, taste, and add more only if needed.
Chill the glass: A cold martini glass keeps the cocktail crisp longer.