You need the transfer paperwork, with the tax stamp. Actually, you need a copy of it. Don't take the original anywhere. Put it away in the safe, so you don't lose it. Losing it would make you be in possession of an unregistered NFA item. Not good.
I don't know what the "certification document" is. The transfer paper is two-sided, and has your picture on one side and the tax stamp on the other.
My stuff gets carried in specific bags. I have a copy of the paperwork underneath the foam, in that gun's case. A guy I know, with many, has copies of all of his stuff in sheet protectors in a three-ring binder, and takes the notebook with him whenever he takes anything out.
Legally you are only required to show documentation to an ATF agent. But if a cop asks for it and you tell him you don't have to show it to him, he will arrest you. Just so you know.
Meddle not in the affairs of dragons, for thou art crunchy, and taste good with catsup - George of Lod, Year of Our Lord 297
I always take precautions.
Beware the Evil Bullet Fairies.