Auto warranties can be bought through two sources; one is the dealer from which you buy your car and the other is from a third-party company that deals in providing the auto warranties. Most of the customers prefer to take the warranty from the dealer because they can be rest assured that the warranty will be updated once the factory warranty expires. The only limitation of buying a warranty from the dealer is that it costs a bit higher than it would be from a third party dealer.
Thus it is highly recommended to do as much research as you can before you call a dealership. It is in your interest to check for ratings and publications of a particular dealer. All you need to ensure is the authenticity of the dealer.
On the contrary there is always a stability factor attached to a dealer warranty, now you may be confused about what this stability is. There are third party companies that are run by under-funded organizations and hence there is large amount of risk involved in dealing with these companies. They may shut down or leave town once you pay then the premium of the warranty and hence you must beware of such dealers.