AWS D1.1(Structural Welding Code- Steel) and D1.6 (Structural Welding Code-Stainless Steel) are welding codes that are not the same as a shop certification program.
However, many shops have welders that have qualified according to those codes. And they likely would do their welding with procedures qualified to those welding codes.

If that is what you are looking for, then I suggest you call the shop(s) you are interested in and ask about their welding qualification practices.

If you are looking for a shop that has been certified as a company to comply with a quality assurance program, then you might want to check out www.aisc.org and look for names of certified shops in your area. Look for the certification links.
AWS also has a program to certify shops in the same manner. I don't know how to check out those except to contact the AWS Certification Dept.
Another possibility is to look for an ASME certified shop. I don't know how to check for those certifications except to ask the shop. Those shops might not use AWS codes but ASME also has very comprehensive requirements for welding.

Hope this helps,
Chet Guilford