Hello Shane;

Take a look at AWS A5.01 / ASME SFA5.01. It lists various test schedules that must be specified to ensure the manufacturer provides the type/level of testing required and the documentation that is deliverable.

The procurement guide, i.e., AWS A5.01/ASME SFA a5.01, tells you what information must be provided to the vendor when the filler metal is ordered to ensure the proper level of testing and the proper documentation is provided when the filler metal is delivered. 

Best regards - Al

Shane,
There is no requirement that a certificate be supplied at all. The label on the packaging, as each of the specifications states in Section 5, is sufficient. What the Section 5's say is that the label IS essentially your certificate (thats why its entitled 'Certification') unless you want more.
As for what is included on the certificate, that is to be imposed by the purchaser based upon the schedules as Al mentioned. What usually happens is that most people just take what they get. They look for chems and mechanicals and a signature and go with it. But there is no requirement for anything unless imposed by PO.