So when those times have occurred I've (we've more accurately) adopted what I refer to the "deer in the headlights" response to just about anything non-trivial. "Hoo boy, that could be doozy. I think someone on the team needs to take an hour or so and figure out what this is really going to take." Then you'll get asked to "ballpark it" because that's what managers do, and they get a number that makes them rise up in their chair, and yes, that is the number they remember. And then you do your hour of due diligence, and try your best not to actually give any other number than the ballpark at any time, and then you get it done "ahead of time" and look good.
Now, I've had good managers who totally didn't need this strategy, and I loved 'em to death. But for the other numbnuts who can't be bothered to learn their career skills, they get the whites of my eyes.
Also, just made meetings a lot more fun.