Warm the limes in the microwave for 30 seconds to slightly soften them (this will make them easier to juice). Cut a thin slice off each end of the limes to make a flat base for each half to rest on. Cut the limes in half and squeeze out the juice into a medium bowl. Using a teaspoon or grapefruit spoon, scrape the remaining pulp and membranes out of the lime halves to make cups (discard the pulp). Transfer the cups to a plastic bag and refrigerate until ready to fill.
Combine the water and sugar in a saucepan and bring to a boil. Set aside to cool. Puree the watermelon cubes in a food processor or blender, then strain through a coarse strainer into the bowl containing the lime juice. Stir in the vanilla extract and cooled sugar syrup. Pour into ice cube trays and freeze overnight.
When ready to serve, turn the watermelon ice cubes into a food processor fitted with a metal blade or a powerful blender. Pulse the machine until the granita has the texture of crushed ice. Fill the lime halves very full with the granita, rounding the tops. Dot with the currants, making them look like watermelon seeds. Serve immediately.