I always tell my tutors that three of the most beautiful words in the English language are "I don't know"--right up there with "three-day weekend" and "bacon double cheeseburger." So many problems arise out of a misplaced sense of certainty that it's refreshing to hear people admit their own sense of doubts, even if those people are ostensibly experts--perhaps especially if those people are ostensibly experts. New tutors--and, by extension, new teachers--often lack confidence: They're not used to being in a position of authority, and it's easy to become nervous when posed a question to which they do not immediately know the answer. Just about the worst thing a tutor can do in this situation is try to fake his way out of the situation.
Doesn't an educator undermine his own authority, though, by admitting ignorance? Not necessarily.
Of course, there are certain things a tutor or teacher should know. I would look askance at a math teacher who didn't couldn't add fractions or an English tutor who didn't know what a thesis statement was. But for the most part, when a teacher doesn't immediately know an answer, there's a reasonable explanation: Maybe a student has worked with another teacher who uses a method with which you are unfamiliar; maybe you're being asked to apply a formula you haven't had occasion to use in years; maybe you're really hung over it doesn't matter! The point is, feel free to admit your own ignorance! Proudly declare that you. Don't. Know.
But. Don't STOP with "I don't know."
After you explain that you don't have the answer to a question, help your students find the answer themselves. If you've attained a high enough level of education that you can call yourself a teacher, then you are obviously not someone who just throws up her hands when stumped by a challenging question. You crack open a textbook, search the Web, even--gasp!--ask somebody else!
The most valuable thing teachers can impart to their charges has very little to do with course content--after all, nowadays the answer to any question is just a mouse-click away. No, the most important thing thing students acquire in school is the habits of mind associated with inquiry, the knowledge of how to seek knowledge. Any time you, as a teacher, have the chance to model these habits, look upon it as a golden teachning opportunity.