Ultimate Ultima fan site ultimaaiera points out that those old saved games you probably have lying around for Ultima 4, 5, and 6 will not work with the freshly released Good Old Games versions of Richard Garriott's classic CRPGS. Good Old Games told the site the following:

"…there are no exact character save files in those Ultima games, but it’s like the “whole game” (like the full folder) is the save game. Can that be true? They told me the problem is that DOSBox is not able to recognize the previous part of the game as a save file (i.e. while playing U5 it doesn’t see U4 as a save)."

The good news is that some dedicated fans are experimenting and leaving comments on the link above. If you don't mind mucking about in your computer, they may have some work-arounds that work for you.