What LIGO does using interferometry isn't exactly like timing as it's more of a differential (relative) thing than an absolute thing.
I would like to point out that _any_ measurement is a differential thing and _not_ absolute. By definition, to measure something means "to compare it with the etalon unit", so it is always relativ to the etalon. Even a wristwatch, or a classic timer as a start/stop counter is still differential (relative) to its internal timebase.
- Another possible method to measure a very short pulse would be a Streak Camera, best time resolution 180 femtoseconds according to
https://en.wikipedia.org/wiki/Streak_camera- Another method might be to measure the very short pulses as a frequency comb to deduce the pulse width. There were some recent Nobel Prize awarded in the short pulses and frequency combs area of optics (these were used to measure time in the range of attoseconds or so, some techniques might overlap with the ones used in streak camera, IDK)
https://www.nobelprize.org/prizes/chemistry/1999/press-release/https://www.nobelprize.org/prizes/physics/2005/summary/
If the OP question was about commercial start/stop counters/timers usually found in an EE lab, then I don't know which ones are the fastest. Also no idea how they measure sort pulses at NIST, but I suspect the shortest pulses might require a more elaborated setup than a COTS timer/counter.
Time related tech, NIST level:
Also from BIPM, but more general:
What exactly has to be measured matters a lot when pushing the limits of technology, so without a goal and a measuring setup example is hard to tell what would be the top available performance.
What has to be measured with that timer? Was the OP question about a specific experiment to measure, or about the best available timer to buy for an EE lab?