Finding out whether an old railroad bond from 1938 still has any value is a tough question to answer. The short answer is that it will require a person to do some homework or spend money on a search service.
Do Appropriate Railroad Bonds Research
The first step would be to contact your broker to see whether they can obtain more information about the company that issued the bond. Keep in mind that brokers typically have access to tools that most of us do not, including Standard & Poor's corporation records, and similar types of resources.
At the same time, consider doing an online search of your own. Try search engines such as Google. Was the company taken over? Did it go bankrupt? If you're lucky, the search will provide the new company's name, address and contact information.
Beyond that, your local library and/or the state in which the corporation operated may yield additional information. Try contacting the Department of Commerce or the corporation commission in the state that is listed on the bond. If nothing else, these organizations should be able to point you in the right direction.
Use a Stock Search/Collectibles Service
If all else fails, there are services out there such as Arizona-based Stock Search International that charge between $40 and $85 for access to their corporate databases, and/or to initiate new research about a company on your behalf.
Also keep in mind that the bond may be a collectible and have value even if it can't be redeemed. To that end, check out Scripophily.com to see whether the security has some collectible value. You might be surprised!
With all of this in mind, remember that spending money involves risk because you may discover that your bond is worth little more than the paper it's printed on.
(Take a look at Old Stock Certificates: Lost Treasure or Wallpaper?)