"Good methods for what? Not certainly to certify that each combination of inputs gives a certain output, as you can read from that paper."
You're ignoring the biggest issue in your whole tangent: real-world engineers with sense won't use NN's in systems unless the problem itself is non-deterministic & other methods don't work. Personally, I push control theory, state machines, ladder logic, whatever for applications like this. You can deterministically analyze them. Whereas, problems with too much uncertainty or requiring approximate solutions will always have an error margin. You personally have been pushing this thread to focus as much as possible on the NN case while ignoring 99% of real-world, use cases representing how the OP topic will usually play out. You also act like the inherent error in the tooling is bad when the problem domain itself has inherent error. So, I decided to address your tangent.
The first solution, safety monitors, goes way back in safety-critical use. That's to have a simple solution checking the ranges or other behavior of the NN that's able to override faulty NN with simpler logic. This can be done for GPS-guided drones that usually move in straight lines or smooth curves. The NN part is reset, diagnosed, or deactivated while the fail-safe system takes plane on simpler path or out of the area.
Second part checks the nets themselves. Again, given a non-deterministic problem domain, the nets will be non-deterministic with the best one can do getting the error margin way down or within fail-safe bounds. This other paper I found summarizes a lot of V&V methods for NN's:
https://people.cs.umass.edu/~btaylor/publications/PSI000008....
Safety monitors. Training data or updates with constraints built in. Automated, test-case generation tweaking expected data. Rule extraction. System visualization. Simulation. All should contribute to safer NN's. They can't be perfectly correct, though, because vision, complex flying, thinking... none of this is 100% accurate no matter what method you use.