A certificate of authenticity is worth nothing if it doesn't come from a reputable and widely recognized authority.
If you go to someone who is a legitimate writer of certificates, they will never charge you for your time unless they are able to issue a certificate.
An appraisal or a valuation is a different matter. In this case people tell you what they think you've got and what it might be worth, and they will charge a fee on that basis.
So it would be better to discuss specific cases rather than generalities ...