I have a different experience on changing a reservation.

Yesterday, Saturday, when I was doing online check-in I clicked on the option to change to a different flight and looked at a later departure for today, Sunday. I was presented with several options at a cost of $0. I picked one, printed my boarding pass, and thought all was well. Was also indicated that I had been placed into the upgrade queue (I am a Platinum).

Last night, I was checking the upgrade queue and saw that my reservation had been canceled. Looking closely at my boarding pass, I see that somehow the reservation system assigned me on the same flight leaving Saturday instead of today. Fortunately a call to United late last night got things restored to my original departure date. Strange that the online check-in would let me make that kind of mistake.

Anyway, back to the original question...when you check alternate flight options on an existing reservation outside the 24 hour check-in window, you will be presented with many options, with both change fees and fare increases if there are any. I know from my past searches, sometimes only the change fee is listed, and sometimes there are options with both a change fee and the fare difference.

Within the 24-hour check-in window, there are sometimes many $0 options. I'm not sure if that has to do with my Platinum or Presidential Plus CC.