Even when a speaker understands, logically, that it's not possible to know everything and it's not even possible to prepare for every question, she often still freaks out at the thought of not being able to answer a question, especially when there are experts or superiors in the room.
You have to get comfortable with the idea that you may not be able to answer everyone's questions -- but you can do your best to point them in the right direction.
Here are a few ways to say "I don't know."
1. Follow up later
This is a great way to stay connected to audience members after your presentation. Say, "I don't have the answer to that right off the top of my head. Please give me your e-mail address after the presentation and I'll get back to you this week."
2. Share resources
Connect your audience members to others who can help. Say, "Here's my answer to that question, but I know someone who can answer it even better. I'll give you her contact information during the break."
3. Make use of present experts
Your expert audience members will love being called on to give assistance. Say, "I see that Janie Expert is in the audience. Janie, I'd love to hear what you have to say about this question."
4. Ask the audience
This is a great opportunity for your audience members to contribute to the discussion. Say, "I have some thoughts on that topic, but I'm also wondering what others in the audience are thinking about this."
5. Give it back to the questioner
Help your audience member do some critical thinking and dig into their own experiences for the answer. Say, "How do you suppose you would handle that situation?" or "What has worked for you in the past?" Etc.
Preparing for the inevitable by having these responses in your back pocket will remove a lot of the anxiety of saying "I don't know." Give them a try in your next presentation!
Please add your "I don't know" suggestions in the comments!
Listen to the recording on SoundCloud: