Other than clearing history/cache I'm afraid I don't have an answer for you to do something similar in Firefox.
Why isn't that an answer?
Just make sure none of the "secret" sites are bookmarked!!!
In Firefox if you right click ( control + click) the search box you will get the option to 'Clear Search History'.
I got the 'Clear Search History' all right, but after I click it and then go to History, everything is still there. Did I miss something?