due to the Security Certificate, at one end or the other, having expired or is not issued by a recognized authority. The DOD is fond of issuing certificates themselves but they are not a recognized issuing authority. Then you get the warning.
There is not a lot you can change in Safari to cause this to happen. IE is a little more lax, imaging that, when it comes to checkin security certs.

Sorry I can be of much help with this one, did you install the Java update recently?