You can click the link at the bottom of the error page: "I Understand the Risks"
Make Firefox retrieve the certificate: "Add Exception" -> "Get Certificate".
Click the "View..." button to inspect the certificate and check who is the issuer.
Only leave the mark in the box at the bottom to "Permanently store this exception" if you trust that certificate.
Click "Confirm Security Exception" to enter the site if you still want to go to that website.

If you can't add an exception, but get a pop-up with the error message then you can check the pref browser.xul.error_pages.enabled on the about:config page and make sure that the value is set to the true (default).

In version 8.0.1 of Firefox there is no option to click on "I Understand the Risks". There is only a "Try Again" option.

Check the date and time in the clock on your computer: (double) click the clock icon on the Windows Taskbar.

• https://support.mozilla.com/kb/Secure+Connection+Failed

For me, when in version 8.0.1 of Firefox there is no "I Understand the Risks" option on my Windows XP machine. However, 8.0.1 Firefox on Windows 7 does show that option. I do not have a solution for the windows xp machine.

Same browser version, same clock time, same website. Windows 7 allows me to add the certificate, but XP does not.

For firefox 12, force it to give you the option of adding the exception.# open new tab and type about:config and press enter.

1. Firefox will make noise about how you will void warranty (crap) we know what we are doing. Accept.
2. In the search box, type the word error and in the results look for browser.xul.error_pages.expert_bad_cert. Note that it is by default false, double click it to turn it to true.
3. Happy surfing, Just refresh the webpage with the certificate warning and you will have the option of adding an exception

edit about:config browser.xul.error_pages.expert_bad_cert from false to true