What would be a good certificate or degree for a product manager in the high tech industry?

Become a Certified Scrum Master. http://www.scrumalliance.org/certifications/practitioners/certified-scrummaster-(csm) It's next on my list and at a very high priority.

There is no certificate or degree in the world that can replace being involved in a good product and shipping a real product. If you have an MBA then you have some of the business background, I would suggest spending your time improving/honing/building your programming skills which is a must in many PM roles. That will be infinitely more helpful than a certificate. If you already are a solid coder, build stuff yourself, ship it, market it (just casually do these). You will develop a good understanding of some challenges in the process and you will develop credibility with your tech and business teams and someone who can handle the process, even the parts they aren't great at. [Also, read everything that Ian McAllister writes on Quora. He's a major PM at Amazon and his advice is top-notch, albeit mostly business focused, not as technical. You can find the tech focus elsewhere.]

While a certificate is optional, some good skills to pick up would be: Agile Management: There are different flavors, Scrum being one of them. Something technical like PHP, Linux programming, Local Area Network setup, server administration (these are more useful the smaller the company that you want to work for is) How to make a good presentation How to network and make powerful business connections (while I wouldn't recommend name dropping, talking to your interviewer about what sort of connections and partners you can honestly bring to the table might help) How to raise funds and structure deals As far as particular programs go, look at summer school, professional and night courses at the colleges and universities near you. If any of them sound interesting, you can register pretty easily, if you're an alum you might get a discount. Alternatively, look at websites like coursera, udacity and edx for an online alternative, which is sometimes just as good, free, and more convenient.

Current credential standards put too great a weight on managerial finesse and too small a weight on technical know how.   So there are ten times as many MBAs in the high tech firms as there should be. Which is why the U.S is losing the innovation race.  The main American inventions are trances (in the bond market)  and leveraged buyouts.