Some websites require a special client certficate for access. If you don't have that certficate, you'll have to contact the site operator to find out how to get one.
Sometimes the problem is caused by a web server that is configured to request an optional client certificate. Safari treats the request as mandatory. In that case, other browsers such as Firefox and Chrome may be able to connect to the site, because they ignore the request.
The first time you were prompted for a certificate, you may have clicked through a dialog that requested access to the Apple certificate in your keychain that is used to secure the iMessage service. In that case, you may be able to regain access to the site in Safari by doing as follows.
Back up all data.
Double-click anywhere in the line below on this page to select it:
com.apple.idms.appleid.prd
Copy the selected text to the Clipboard by pressing the key combination command-C.
Launch the Keychain Access application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Keychain Access in the icon grid.
Paste into the search field in the Keychain Access window by clicking in it and pressing the key combination command-V. An item may appear in the list of keychain items. The Name will begin with string you searched for, and the Kind will be "certificate."
Delete the item by selecting it and pressing the delete key. It will be recreated automatically the next time you launch the Messages or FaceTime application.
The next time you visit a site that prompts for an optional client certificate, cancel out of the prompt. You may have to do this several times before the server stops asking.
Credit for this idea to Christian Braukmueller of SAP.