Find a part of the question you are comfortable answering if answering the whole question is not an option.

This may sometimes be enough to satisfy the other person.

Buy yourself some time by stating that you don't currently have enough information to provide a solid answer.

Turn around the pronouns to shift the focus on the other person and take it off of you.

For example, you can use: "It’s interesting that you think that" or "‘Why is this question of interest to you?"

Acknowledge the question, but then divert the conversation to a different topic, one you are more comfortable approaching and that interests you more.

Use phrases such as "That’s an interesting question, but I’d like to point out…"

Difficult questions tend to be emotional because the asker is usually frustrated or anxious.

So it might be a good idea to give the other person some control over the discussion. For example, use "I understand you’re frustrated. Would it be helpful if I shared some information about that?"

Make sure you maintain a polite tone, even if you refuse to answer the question.

Also, mare sure you give out extra information and don't just answer the questions with a “yes” or a “no”.

The way you hold your body is as important as your tone.

Avoid poses that make you seem defensive (crossing arms or avoiding eye contact).