Preparation: Cut limes in half lengthwise; cut around pulp of each half with a sharp knife, leaving peel intact. Scoop out pulp, using spoon to loosen pulp from peel, and reserve 2 tablespoons of lime juice for Granita. Set lime cups aside. Stir together sugar and water in small saucepan; heat to boiling. Cool slightly. Place watermelon in container of food processor; pulse to puree watermelon. Place colander over bowl and pour puree into colander to strain out the seeds; forcing watermelon through with back of spoon., if needed. Stir reserved lime juice and cooled sugar mixture into pureed watermelon. Pour into 13x9x2-inch pan; freeze until firm, about 4 hours. To serve, scrape frozen watermelon mixture with spoon to make Granita. Stir in currants for "seeds." Mound Granita in lime cups; serve on bed of crushed ice.