[Shinmon]

You are being asked those questions because you are seen as an expert in the matter or as an "authority" (by expertise) in general.

First, I think it should be okay to answer "I don't know" if you don't know. If you feel like this is okay it should become easier.

If you lose confidence when your managers are around I would start asking myself why this is the case? Are you afraid that they will judge you? Do you have a strained relationship?

Anyway, this is a rather complicated issue which takes time to tackle. If you can afford it, go see a public speaking coach/mental coach/therapist. If you think it's just part something you need to practice, there are "impromptu theater" groups.

[Zanni]

Seconding "impromptu theater." Or, as I was going to say, improv comedy. Improv will make you much more comfortable with 1) trusting your instincts, 2) keeping your cool when you can't immediately think of what to say or get an unexpected reaction to what you do say.

If that doesn't sound like your jam, maybe look into a speech class or Toastmasters. I know you're already comfortable speaking in front of large groups, but you'll have an opportunity to practice extemporaneous speech (speech with very limited prep), which should be directly applicable to your situation.