Couldn’t get past the cheap verisign certificate on a site I need to use. Yes, there was a work-around to get it into the trusted list, but that sounded like a recipe for disaster.

Browser issue with SSL warning about invalid security certificate - Ask OLPC

There other option - install a special XO version of Opera.

Opera OLPC Edition
Opera has made a special Opera OLPC Edition package. Screenshots are available here.
Opera is more than a secure web browser, it’s also an RSS and Atom feed reader, bittorrent client, email client, and IRC client. It also has many keyboard shortcuts that make navigating on the XO easy.

Opera OLPC Edition - Desktop Team - by Desktop Team
This is a special edition of the Opera desktop version - the Opera OLPC Edition. We have been testing Opera on the OLPC laptop since we received the “lean-mean-green-machine”, as some here at the office like to call it.
.. although there are install instructions here - I followed the wiki.laptop.org instructions

The install went really smoothly. I added a bit of information to the instructions - how to tell when the download is done.

There is still an error message that comes up - visible on exiting Opera in the Terminal activity. Sounds like whining but not too serious and doesn’t appear to impact browsing as far as I can tell, but it is worth watching.