Old public clocks sometimes use the mains frequency as a clock signal to maintain correct time. At the end of the day, the power authority is supposed to adjust the signal slightly to make sure these clocks maintain the correct time.
So I built a device that analyzes mains power supply phase variance with microsecond resolution. It's accurate enough that I can see the power authority turning on and off supplementary turbines to keeps the mains frequency correct.
That's how I determine my level of trust in public clocks.
Well, that and maintaining sub-relativistic velocities relative to them. Which is pretty easy honestly. If you're having problems with this, you've probably ceased to be biology or chemistry and started being physics. So you probably have more pressing concerns than keeping time!