If you mean the actual paper marriage certificate, I just filed mine away with all the divorce papers. Divorce is a hugely legal thing, keeping the papers around seems like a good thing.
I’ve just got a big envelope with all the papers in my filebox. Never have needed it, might never need it.
Okay, let’s expand the question a little. Thanks to Belrix for raising the need for some clarification.
The friend has the legal marriage certificate, and the religious marriage contract. The m.certificate is a public record, AFAIK, and as UnwrittenNocturne noted copies should be publicly available. The m.contract is a private record, no copies available anywhere, and (at least in this case) is very artistic.
The question thus becomes a two-parter: What do (or did) you do with the civil certificate? And what do (or did) you do with the religious contract, if you have (or had) one?