The Paper Anniversary?

Well, most newspapers keep back copies. You could get a copy of the paper that was published on the day you got married, or maybe the 2 papers that were published on the day that each of you was born. (if you can't get them directly from the newspaper, there are internet companies that can supply them).

Or, there are companies on the internet that will name an un-named star in the solar system after your loved one. You get printed certificates, plus a map of the sky at night showing where your star is, and other stuff. It's probably phoney, but, hey, it's a romantic idea.

Or, get a copy of your marriage certificate enlarged and framed?

Origami?