The best estimation system I've seen is to actually BET on the completion date, closest gets a free lunch paid for by other members of the group.

Those dates were mostly informed guesses of what would actually happen or go wrong. Importantly this was between friends. Needless to say, they turned out very accurate.

I could see that working well for managers, if they incentivize estimates as biweekly or monthly bonuses going to the most accurate one, and each person gives a detailed estimate of ballpark plus probability of what sorts of things can go wrong and how that impacts the estimate.