Author's email address in a published paper is not working
There's no particular "protocol"; just try to find some other way to contact them.

I would try:


Google the author's names.
Look for more recent publications by the same author(s); see if they list updated email addresses.
LinkedIn was a good idea.
If you have found the author's employer, see if you can find his contact info on their website; or contact someone else at the company and ask.
Some professional societies maintain a database with contact information for all members.  For instance, mathematics has the Combined Membership List.
Contact someone at the previous employer and ask if they have current contact info.