This is where the Internet can be useful. Then try other search engines. Different search engines use different criteria in both finding and ranking hits. Search for not only the exact trademark, but also variations such as common misspellings, truncations, abbreviations, and phonetic equivalents. Search engines with Boolean logic capabilities may help.
Many search engines have links to such directories.
Again, use more than one directory and include variations on your trademark. Once you find a domain name of interest, check to see if it is active by entering it as a destination address for your web browser. Evidence of a diligent policing program could later prove valuable. Once you find hits of concern, you need to determine your rights. A trademark lawyer can help you evaluate the hits.