I say it exactly like that. "I don't know, but I'll find out and get back to you."

They key isn't how you say it, the key is that you consistently do it so that people learn that when you say it, you mean it.

Yes, precisely. OP, you're overthinking this. As a consultant I talk with a lot of people, nobody whose opinion you care about will think less of you for saying exactly that.

An intermediate answer you can give is something like "I would take such and such steps, but I'm not sure this will solve the issue and I need to verify this offline". Don't bullshit people, it's a small world, it's almost never worth it.

If it is relevant, I tend to take very good care to understand the request. I ask follow-up questions, take notes, etc. Not only it is useful (understanding the problem is key after all!) but it will show you care, and that your "I don't know" is not synonymous of "I don't care" or "Just open a fucking ticket".

This. I add to it sometimes, "I don't want to tell you something now then go back on it [when I thought about it properly]".

Because how do you challenge this? Insist someone should know an answer without thinking? Insist their guess should be the same as a thoroughly thought out answer. At the same time you're not being evasive, or saying that you have no idea. You're stating you want to deliver a high quality answer first time round.

Even if people push back on this, you made it clear you're offering a guess, not a considered opinion. Nothing wrong with providing a clearly labelled guess, then changing it later.

Agreed. I usually add "...by the end of the day", "...after my next meeting" or whatever I feel is the appropriate timeline to find the answer to their question and then follow up.

If you keep your word consistently, people will trust you and the conversations will become easier and easier.

Yea, I think the wording in the title seems fine.

I probably end up slightly wordier...

"Hmm, not sure. My best guess is that we're probably pulling some values from context and then using that to determine the behavior you're seeing, but I know my manager has a few contacts on that side of the org, I'll reach out to her and get back to you, probably in the next few days"

And then yea, just... delivering on what you say you're gonna do or updating if there's some bends in the road you didn't see.

Yup yup basically this. Being consistent is great but I'll be pedantic and say the key is actually following up and then also being right.

As far as how to do it confidently? The same way you say "that is a tree" when you're looking at a tree. You're 100% sure you don't know, just say it. The rest is probably in your head. That's been my experience at least.