It sometimes happens that major airlines results listings feature a page, but the site is not there: can anything be done? When you see this sort of thing, you can use the cache feature of the listings to view the site as stored by the search engine.
If you are searching for major airlines web resources you can find sources to be had to use along with your normal searching method. These would include the categorized directories (which were once common), social bookmarking sites and blogs.
Everyone uses search engines. Here's a tip: it can be very useful to find the latest results. Using 'by date published' advanced searching settings during a 'major airlines' search will allow you to find the newest result pages. Your favorite search engines will in addition have a 'find pages like this' option to display more closely related pages to have a look at.
While seeking major airlines pages you could also look at a web directory service like DMOZ where sites have been checked by human editors. A few years ago using such a link collection daily was normal but it's seen as old fashioned now as search engines seem to give you more control.
Major Airlines web and web 2 sites are, of course, not all the same. You will have to get to the top-rated major airlines web and web 2 sites as fast as you can. On getting to a site, if there are suddenly lots of pop-over ads or whose sole purpose is to get your email address, then you can just say goodbye.