In a saucepan bring white wine, Sherry, honey, and sugar to a boil, stirring until sugar is dissolved. Transfer syrup to a heatproof bowl and chill until cold.
Cut peel and pith from grapefruits and oranges and cut fruit into sections, discarding membranes. Halve pomegranate and squeeze gently to yield seeds with juice. Divide citrus sections, pomegranate seeds and juice, and wine syrup among 6 dessert bowls and chill, covered, at least 15 minutes and up to 1 hour. Stir compote before serving.