In my municipality, you're not supposed to alter the permit at all, unfortunately. A common workaround here is to make a copy of the original permit, write "copy" at the top, laminate it, post it in a public area, then file away the original.
I would if I had to keep it displayed where anyone could read it, such as a liquor license, a firearms dealer license, a tobacco distributor permit, or something of that nature.
Do you mean when they're issued?
In that case - no. We email them, and if someone requests them in person, we just print them. I know that in the "before times" they would get put in a plastic card slip thing, but not laminated. I haven't seen anyone do that on site either.