I can only speak for a domestic cleaning client but in my experience they take my word for the insurance documentation. Having said that I always take the certificate with me on the initial consultation - just in case. I definitely go through the cleaning schedule with them and ask them to read through my t's and c's before starting any work.
I don't do anything regarding COSHH so I would be interested to see what others' opinions are on that. Is there a special document that should be presented, for example?