How do you prove that a ballot was mailed on time?

Several states allow ballots received after Election Day to be counted. Some of them require proof that they were mailed on or before Election Day; others do not.

You can well imagine the room for mischief if no proof is required.

One way to determine if a ballot was mailed on time is the postmark. However, not all postmarks are legible. So the question becomes how do you prove that a ballot was mailed on time? Obviously, if a postmark is not required, then there is room for additional ballots to be produced that could help the losing candidate.