If you have a cantab.net account then you can import your mail from Hermes to your cantab.net account. Log in to your cantab.net account and go to Options -> Import External Email. Migrations take a while so, if you are leaving the University, be sure to queue up your folders at least a week before your account here expires.
If you can't do this, or don't wish to, then in general you can move email from your Hermes account to another mail account by setting up both accounts within an email program such as Thunderbird or Outlook. Once you have access to both accounts, you can simply (depending on the email program) drag and drop, or copy, emails from your old account to your new one. You could also drag the email down to a local folder on your computer and then back up to a new mail account once you have it set up. More detailed instructions for saving/archiving your email to your own computer are available for:
Another option is to forward the messages you want to keep to your new account. However with many email programs the messages you forward will appear to come from you rather than the original sender.