What should I do with award certificates?

Give it to a relative (parent, spouse?). My mother has a "wall of Sergio" in the house where she displays different types of significant awards, letters, etc. I think it's a little weird, but giving them these awards is a nice way to let them have a handy reminder of what you're up to at the time, and parents certainly appreciate it sometimes. My mother and I came from not very much at all, so she is so happy to hear I am doing something with my life -- maybe your family may feel the same.

You will probably never in your life need the physical certificate.

If you don't want to hang onto it, you can probably just dispose of it (though you might as well scan it first).

I think you should, for documentation, keep everything that provides proof of your career achievement. One or two folders should be sufficient for most people. You never know when it would be useful to have that handy. It's just a piece of paper, and I would keep it where you keep official or semi-official documentation about your career. It's less space than a trophy, in any case.