I am presuming that you manage the system which is receiving the emails.
It all depends on what kind of devices do your edge smtp acceptances (your MX devices).
For us, we have anti-spam devices as our primary MX devices. These devices are fairly good for logging and with a little cleverness and a lot of patience we can figure out if a particular email got received and where it went from there.
Sometimes it requires cooperation from the sending system's administrators -- they should be able to trace the email leaving their network, and be able to tell you when it left their network and where it landed after that. Unless there is a more complex mailflow defined, mail should leave their edge systems and land on one of yours. Using that information you should be able to pick up the trail in the logs of your systems and trace it either to a mailbox or to some place in the flow where it stopped or bounced or got misdirected.