What license/certifications are appropriate for mold remediation firms?
The Illinois DPH site related to mold, which does not specifically license remediation firms..  They also don't do inspections.  They DO list several internet sites for contractors:

The Institute for Inspection, Cleaning, and Restoration Certification 

and 

Association of Specialists in Cleaning and Restoration 

neither of which are specific to Illinois, but do allow zip code searches (I found IICRC friendlier)

A helpful site at the EPA for mold:  In their Mold Cleanup section, they recommend that the remediation contractor follow their Mold Remediation in Schools and Commercial Buildings outline (even though its your house, not a school).  

It might be a pertinent question to ask: "Do you follow the EPA guidelines for remediation?". 

A basic tool for your own use, a moisture gauge, will tell you if the area is ready for treatment:  Wooden interior framing should be &lt; 15% moisture content.  One reasonably accurate meter (non-contact) is the Ryobi E49MM01.