With typical cold browning solutions (Wahkon Bay, Mike Lea's etc.) I just throw a handful of grocery store baking soda into a tea kettle full of water, boil it, then douse the browned part with it - keep pouring it over the part until it becomes too hot to touch - and while still hot (it will basically dry itself at this point from the heat) give it a quick wipe/rub down with motor oil on a soft rag. I have not had any problems with rusting continuing beyond that point and the finishes have held well, and I live in a fairly humid climate (Ohio Valley).
Guy