Add the water, wine, and cinnamon sticks to the pan; sprinkle the sugar over the quince.
Bake the fruit in the preheated oven until lightly browned, about 35 to 40 minutes. Turn the quince right-side up and bake until tender, about 10 more minutes.
Remove the pan from the oven and let the quince cool slightly.
Transfer each quince half to a plate and drizzle with a tablespoon of juices from the roasting pan and a dollop of whipped cream.