Where are the save files located for Ultima IV save games?

Look for the *.SAV files in the directory where you installed the game ("C:\Program Files\GOG.com\Ultima 4\" if you used the default location for the free download, or "C:\Program Files\GOG.com\Ultima Second Trilogy\ULTIMA4" for the IV-V-VI compilation).

if there not in C:\program files\ then try checking around c:\users\app data\ and it's sub folders.

Found 'em! Thanks for the help, fellas.

you posted to say you found them but didn't bother to say where.
AWESOME!

Since the other user didn't actually tell us where he found 'em, and it seems none of the forum messages actually mention where they really are in a modern GOG supplied installation as of 2021 (there are mentions of ux4, which are not GOG supplied), I'm adding it here (also so that I have something to look up again if I ever forget.)

On my computer, it was in:
<game install>/cloud_saves/

Since various *.SAV files exist in the <game install> directory, and they don't seem to get updated, I was sitting there quite a while scratching my head until I noticed the cloud_saves directory.

So there you go.