Managing personal Outlook.com account settings, security, and privacy
There's another trick that works for me about half the time. I have Outlook.com bookmarked on the Firefox bookmarks toolbar. After signing in to Outlook.com, when the secure connection error message appears, I just keep clicking on the Outlook icon on the toolbar, and after about six reappearances of the error message, the "opening your inbox" page appears, and it works. If clicking on the icon doesn't work after a dozen times, sometimes closing the tab and opening a new one, then clicking, works.
I have no idea why this works, and only some of the time.