Incorporations, Colorado:
County (varies) assessors' offices; archives for historical county mining claim documentations.
Stock certificates from early mining companies (1800s-1910s) are often without value, but you never know.
Monetary value as stocks? Check:
Value as collectibles, historical artifacts?
Is the mine significant? Does the stock certificate include signatures of famous people? Is it rare? You can do some historical research using the resources listed here; and check out websites such as Scripophily for collectors' pricing.
Personal value ("for fun")?
Mining company stock certificates are a part of mining's history. They can include beautiful graphics, famous mine names, far locations. Collect and enjoy.