When all the treasures from your child’s activities arrive home, where are they going to go?
It’s nice to display the most recent one on a shelf of dresser top. Everybody likes to be reminded of accomplishments. Beware of displaying many, unless you have a glass-fronted case; they are not fun to dust.
Consider keeping a plastic bin for each child. If you have the mental limit of one bin, it encourages prioritizing and editing of the old trophies when the new ones need to squeeze in. You may be able to place a smaller box inside for tiny or delicate things that could be lost or crushed. And if you choose a box with rails for hanging files, you could add a few hanging files for certificates, swimming level reports, or pictures, to save them from becoming scrunched.
These types of bins usually have lids, fit nicely into closets, and stack well.