There are several sites that offer Clan & Tartan Searches. Often you'll do better to go to an actual Celtic Festival that has a Clan Row.
From there you can be assisted by Clan representatives.
Most of these can best help you lookup your Clan or Tartans with their more specialist books and databases.

Here are some general sites you may reference:
Scottish Clan and Tartan Finder on clan.com
Welsh Tartan Search
Irish Tartan Search
Tartan Finder at MacGregor and MacDuff

Find Your Local Celtic Festivals:
Local Highland Games and Festival Listings