Question: How can I get rid of the Internet Explorer's certificate expiration pop up window. It's really annoying.
Answer: If it is your certificate then renew it.
If it is someone else's certificate then their page is no longer secure. When an expired certificate message pops up you should always select cancel so as to stop loading the page as the expired certificate indicates that the page is no longer secure. If the page is one that you really need to access then email the site owner and request that they renew their certificate so that you can once more access their secure page.
The certificate expiration page is your friend.
The one and only situation I can think of where it would be appropriate to proceed past a certificate warning is where the message indicates a mismatch between the site that the certificate was issued for and the site that you are trying to access. You would only proceed in this situation because you already know in advance of the message that the certificate mismatch exists. This would apply for example if you are attempting to access webmail on your own hosting where the domain name you use is your own and the certificate identifies your hosting provider. In this type of situation you know about the relationship between the two site because you are the one who set it up. You should still want this message to pop up though as in this instance the certificate popping up and identifying the expected mismatch is almost as meaningful in confirming that you are accessing the right site as not having such a message appear when you access someone else's secure site. Note also that in the case of a certificate belonging to a known different site that is on the same server that the certificate still provides all the same security through encryption as if the certificate were for the correct site.
This article written by Stephen Chapman, Felgall Pty Ltd.