Well, I'm still in the USA -- I haven't gone to Tokyo yet. And my wife will join several months after me.
I don't recall anything about the CoE...sorry if this doesn't help much! I suggest asking the Embassy, since the information should be reliable from them
They never asked me for a marriage certificate, either. I believe they will simply need her passport information for the visa, but no documents required to prove our marriage.
Which country are you applying from? And which universities are you applying to?