You can both cancel a held ticket and refund a purchased ticket online.

For a held ticket, go to "my itineraries." Then hit the, "view past trips" link. Once that page comes up (and the computer usually takes a while), find your held itinerary, open it, and hit the cancel link.

To refund a ticket within the 24 hours, just go to the ticket refund part of ual.com. Find your itin. And request the refund.