Is there a popular provider for doing this? It sounds like a lot of work to find a solution in which both parties trust (both technically versed and reliability wise). A common notary probably wouldn't cut it, right?
There's a bunch of companies doing it, some dedicated, some as part of larger related offerings. E.g. I know NCC Group (large IT security company) does offer it, TÜV (which does all kinds of certification and compliance work), ...