The Socratic method can also be used to cover up your own ignorance. Simply throw someone's questions back at them and let them come up with the answer.
For example:
Supplicant: "Why does my head hurt?"
You: "Why do you think your head hurts?"
Supplicant: "It could be because I just hit myself on the head with a large hammer..."
You: "Your head hurts because you just hit yourself on the head with a large hammer."
Supplicant: "Wow! You're so clever!"
Despite the somewhat stilted/simplified dialogue, I believe you get the idea.
(Please note: This will not always work, as people can notice what you are doing, and get angry - or turn it into the Game Of Questions)