Selenium 2 Webdriver will ignore certificate errors by default.

Just in case you still have problems try this:

Chrome uses the native operating system's system-wide certificate system, so if you add an exception for your certificate using the native OS controls, it should all work.
To do this in Windows, grab a copy of the certificate (click on the yellow triangle in the address bar, press "Certificate Information" > Details > Copy to File, save it somewhere.
Then wrench menu > Options > Under the Hood > Manage certificates and import the certificate (probably as a Trusted Root CA).

On IE do the following:
Go to Tools----Options---Security Tab

Select Local Intranet, Trusted sites and Restricted sites and Update the security level to low for all the three. Check the attachment.

This will apply system-wide - bear that in mind when using IE, Chrome, or any program which uses' the system's certificate store.