I think I found a candidate for the male's side of the arms:
http://www.chgh.net/heraldik/s/sp/spiessc.htmThere are several branches of this family, most were not far from Zurich. I also found one branch which named a lot of people around 1672 Hans Konrad (Conrad) Spiess. I could find no direct link with the Barmettler family, but there are still some of the Spiess family in Zurich. I realize the arms shown aren't exactly the same as the ones on the cup, but I also saw one almost the same some time ago. If I remember correctly it was an anglophone posting by someone who identified the arms as that of the lance or lanse family. Since the S didn't match L, I didn't make a note. Now of course I see that Lance is just a translation some anglophone made from the German Spiess. Unfortunately I can't find the posting and don't know how I found it.
Maurice Meslans