How to prove that an email has been sent?

"Unfortunately, as with physical letters, proof of sending is not proof of receipt.

While the e-mail shows as sent in your mail client and it will probably be shown as sent in your ISPs mail server, there will be (many) other mail servers between there and the final recipient. At each one of these the e-mail could have got lost or delayed, so it could well be that your landlord's estate agent is telling the truth (though I'll admit it's more likely that they are lying).

To have proof of receipt you'll need the equivalent of registered post here in the UK where the recipient has to sign for the letter."

You could try contacting the real estate agent's ISP and ask them to provide logs. If the logs show your email, then, you proved you sent it to the agent. Of course, the agent can still claim to have not received your email.
You could try contacting the real estate agent's ISP and ask them to provide logs. If the logs show your email, then, you proved you sent it to the agent. Of course, the agent can still claim to have not received your email.

"There is a new service (that I'm affiliated with) called The Evidence. Basically you append a wildcard to the recipients email address called an eEvid.

For example, if you were sending the email to john@smith.com, you would actually send it to john@smith.com.eevid.com. When the email gets to John Smith there is no indication that the email has been tracked (John Smith doesn't know) and neither does it ask John Smith to do anything. He is completely unaware of the fact the email has been certified. As the sender of the email you are immediately provided with a Certification of Proof (by email).

It's free for a limited use account."

"I can't help you with this particular case, much more than the others did that replied to your post, but I have a good suggestion for the future.

You can use copyconfirm.com.

It's an easy tool that exactly solves this problem. You can easily prove what you sent, when you sent it and to whom. I use a private account so it costs you nothing (if you don't use it too much..)"