Not much to add to the already given good advise. You did not say if you live in a high humidity climate or store your razors in the bathroom which would amount to the same thing. For the former take the extra precaution of oiling your blades post shave and for the latter don't store them in the bathroom. I do not live in a high humidity climate and don't store my razors in the bathroom. I do all the previously given advise but not the oiling and have had no problems with rust on either my carbon or stainless blades.

When stainless rusts it is usually just sort of staining and any metal polish should take care of it. Metal polishes like Mothers Mag and Aluminum, Flitz and the like.

Bob