Search the name of the company that issued the stock or bond on the Secretary of State's website in the state where the company was located. That will tell you whether the company is still in business. If yes, contact the company. If the security identifies the state in which the company was incorporated, and it is different from the state in which the company was located, search the Secretary of State's website in that state as well. Companies do not have to incorporate in the state in which they are located. If your search(es) indicate that the company is no longer in business, try the following suggestions.
WSU Libraries has one publication that lists obsolete securities. It is Annual Guide to Stocks. Holland and Terrell Reference HG 4961 D56 2003.
The U.S. Securities and Exchange Commission also has information on Old Stock and Bond Certificates.
Washington State Department of Financial Institutions provides information on Old Stock Certificates.
ipl2 provides suggestions regarding Old Stock Certificates.
Investopedia has an article titled Old Stock Certificates: Lost Treasure or Wallpaper?
