I have let my mind wander into a silly state and started imagining refunds or replacement guarantees for library services

If we can't answer your question we'll give you a coupon for $5 off your city taxes that support our services.
If the information we have provide proves to be unsatisfactory, you may move to the front of the queue at the reference desk.
If we fail to notify you that a requested item is ready for pickup we will forgive existing fines or give you a coupon to use to pay future fines.
Seriously though, I have thought of some stuff that might qualify as an "assurance" in a library:
All users of reference services are given a card with contact information for follow-up questions and in the case of phone reference all callers will be asked if they would like to provide and email address for follow-up information. All email reference includes a "signature" with information on how to contact the library for follow-up questions.
If an interlibrary loan request is going to take longer that the libraries average turn-around time you will receive an email notification.
I think that these sort of assurances are part of standard services for some libraries, but we could improve customer services by making them explicitly stated assurances in our representations of our services.
Just some thoughts.....
Sheila