Betty, when I first read the title, I thought you meant for long term storage, but upon reading your post I realised you mean for temporary purposes, like when you have pens inked with different colours and you're writing a snail using all of them sequentially.
Well, for that, I think generally you are supposed to keep the pens with the nibs facing up. I think also that modern pens can last longer with having them lying around horizontally without any leaking of any kind, but especially for vintage pens I think it is advised to have them kept nib upwards.
I guess it also depends how long you intend on keeping them inked and unused for, as I think that it is probably safer not be left like that for too long (a week or two?). Of course, there are plenty of examples where pens can still write after many, many weeks of "rest", but I'm not sure if any of the experts would actually advise that.
I try to always do this with all my pens anyway, vintage and modern, all upwards in a cup or shirt pocket, just because I'm AR that way.
Just in case you haven't read it yet, have a peep at the Binder bible here for general pencare (actually I'm not sure right now if he mentions how to best store inked pens here):
http://www.richardspens.com/?page=newp_pel.htmG.