A few years ago I measured my longitude myself, just for fun. I measured the time of local noon, using a portable shortwave radio tuned to WWV. Correct local solar time to mean time with the equation of time, read off my longitude. I would have won the prize. Shows what an accurate clock can do.
I've read Captain Cook's logs and in his time they observed things like the moons of Jupiter to get a time reference. Reasonably accurate, but time-consuming.