Out of Bounds Punts - How do the spot the yardage?

We’re talking American Football here.

So a punter angles his kick toward the sideline to try to pin the opposing team as close to their own end zone as possible. When it goes out of bounds, the referee on the sideline blows the old whistle and starts trotting up the sidelines while looking, whistfully, at … something. Then he stops in his tracks at some point, puts his foot down and declares that that is the precise spot the ball went out of bounds … even if the ball went out at the point but 40 feet in the air.

How the hell do they do that?

By using their best judgment, I assume.
Whenever the ref starts walking down the sideline until reaching the spot, it reminds me of the Cliffhangers game on The Price is Right. The suspense keeps building until the referee or mountain climber finally stops. Sometimes I even hum the yodeling tune they play on TPIR when I see a referee making the walk.

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They work as a team and estimate based on trajectory.