You could try forwarding them to a separate account?
Of course, if you're really wanting them for long-term storage, the only good solution is to copy the emails into plain text. Plain text files open up just as good today as they did 25 years ago, and EVERY operating system can view plain text files, and likely computer systems 25 years into the future will be able to read plain text as well. There aren't "encoding issues" or version incompatibilities like you'd get from a word document. The text files themselves end up only being a few kilobytes. It's cross platform, too so if you are ever forced to switch from Mac, you can be sure that Linux, Unix, DOS, Solaris, Windows, ChromeOS, iOS, Android, WebOS, Windows Phone, etc, will be able to read the text file.
You can just copy all of the text to a TextEdit (on Mac) or Notepad (on Windows) document and call it "emails from grandma.txt" or whatever. Include dates and times, replies and anything else that you want to have saved (you probably don't need email headers, etc).
If it's that important to you, plain text really is the only solution.