How are barometric pressure measurements traceable over centuries to 100 parts per million accuracy?
Mark's answer about mercury barometers is correct - but it is not the complete story.

Barometers were initially constructed using water, not mercury, on the manometer principle.  Water is lighter than mercury, so a water barometer requires a 10.3m tube.  1mbar is therefore roughly 1cm, and 0.1mbar measurement is clearly trivial using a ruler with 1mm gradations.  Of course the exact units of measurement would depend on the country in which the measurements were taken, but it should be clear that measurement to this precision was perfectly possible, albeit with an inconveniently-large barometer!

Mercury barometers, with around 75cm height of mercury at 1bar, were significantly more convenient.  As Mark says, this does require a much more accurate ruler to measure it though.

But the accuracy of a simple ruler is not the complete story either.  The Vernier scale was invented (or at least popularised) around the same time.  With a floating Vernier marker, mercury barometers could be read accurately to around 1/10th of the ruler scale.  For a ruler marked in 1mm intervals, a 75cm column of mercury could therefore be read to 133ppm accuracy, which is close enough in accuracy to the original water-based barometers.