When you come up something you need to know, most search engines give you what you need. Reverse yellow pages is an extremely helpful service that is used by millions of people who need to find out the name/identity of an unknown person or business, as well as any other information they may require such as a phone number, address, location, etc.
Doesn't the government have access to these mythical tools that give them the ability to find anyone, anywhere, and even find unlisted phone numbers, you would think so. If you think you'll be using the directory frequently, just add it to your favorites and you'll be able to head there directly from then on. The difference is the classification of the information.
This will mean that your search won't be free, but the fees for a reasonable premium cell phone service are never very expensive. Even with the free residential phone number search you can find out the details of which phone provider owns that number and in which city they are based and this may help you recognize the number. If you haven't yet ventured online to find a phone number, find one of the online residential phone number search engines and try it out.
Cell numbers are typically harder to track down and you won't find them in a free service. To summarize, if you want to trace cell phone numbers free directories are not going to help you.