Searching for lost .pem file in time machine back up
To retrieve the .pem file you need to locate your backup folder and traverse its directory tree, since it has the exact same structure as what your OS had when it was being backed up.

Some files and directories might have a red sign in the bottom right of their thumbnail, which just means that you need to enable access rights, which can be done like this:


Select the file or directory with the red minus symbol.
Choose Get Info.
A new window will appear, make sure the bottom right lock is open (if closed, click on it).
Click on the + in the bottom left corner.
Another window will appear, find your account and double-click it.
Restore the bottom right lock to its former state (important for security).