...on my SGSII?
AT&T says software is up to date. How would I add the certificate signature myself, and doesn't this defeat the purpose?
It doesn't matter which phone you have in this case, but Android version does matter. You need at least 4.0.x to install a certificate.
First you'll need a copy of the certificate. Android browsers don't let you install the certificate directly like some desktop browsers do. I haven't found one that could save them either, so here's how I did it.
Open the site on a desktop browser. I used chrome, but you can use IE, too as long as you run it as administrator. Once you bypass the security warning you should see a red icon in the address bar. On Chrome it's the lock with the red "X" on the left, on IE is a red shield on the right. If you click on that it will give you the details of the certificate and you want to click the "certificate information" link.
You want the "details tab and you should see the button to copy to file. Select that and an export wizard opens. Accept the defaults until it prompt you for a filename/location. For now pick a place you can find it and a name you can remember. Just call it by the website name with no extension and put it on your desktop. the wizard will append the ".cer" extension.
Once you've done that, you then have to copy the file to the root of your sd card which will be your internal storage.
On the phone go to menu>settings>security>credentials storage and choose install from sd card. Now here's a gotcha. The security policy will not let you install untrusted user certificates without first having a screen lock in place. Pattern, PIN or password. Once you set the password for the screen lock, your certificate installs and you're good to go.
Of course you now have a screen lock, so it might just be easier bypassing the warning instead of installing the certificate.