In a post apocalyptic setting, rebuilding humanity's technologies would be a pretty prevalent idea. I am in the process of becoming a mechanical engineer. Something that I have noticed is most classes don't teach how to make persion tools from scratch. How would someone, given unlimited raw resources but no references(rulers,tools,ext) be able to build something like a persicion lathe or a vernier scale?
In many cases it is possible to make measurements to a much greater degree of precision than the parts required by the instrument doing the measurement. Just think of things like plumb lines, spirit levels, dividers etc and once you can get straight lines and circular arcs you can do pretty accurate geometric constructions.
Also techniques like lapping and honing naturally tend to create geometrically precise surfaces on flats and bores respectively and don't require precision tools.
Another example is white metal bearings where a low melt allow (eg Babbitt metal) is cast into a bearing surface and then scraped by hand to fit a shaft.
Similarly when making parts the first priority is that they fit relative to each other, this doesn't necessarily require very accurate absolute measurements. One fundamental technique is to offer up tow parts with one of them coated in marking blue or lamp black and use that to see where any high or low spots are then carefully scrape or file them down and repeat. Indeed similar techniques are still relevant today for things like refurbishing machine tools.
There is a good book on this subject called The Art of Blacksmithing by Alan W Bealer. This includes a lot of techniques used by fitters on steam ships which due to the need to make improvised repairs with limited resources was one of the last trades to use traditional hand-fitting techniques.
Often apprentices would make many of their own tools as part of their training.
The problem with this approach is that any one set of parts only fits with itself. To get the interchangeability of parts needed for proper mass manufacture you need a standardised system of measurement and tolerances. For obvious reasons screw threads were one of the first things to be standardised.
So in summary geometric tolerances and fit come first than absolute measurements.