with a saw attachment. Cut the wood a few inches above the rot. You can find trim, brick moldings, etc at most hardware stores and cut pieces to fit. Caulk or bondo gap between depending on how well you matched the cut line.

Almost as much work as replacing the frame, but you don't have to deal with hinges, lockset locations, etc. Been on several historic restoration sites where they do this to save as much of the "historic" material as possible. Very good results.