SMTP is a best-effort delivery system and it can take quite some time. Especially these days when there are several content filters between the sender and receiver. Many mail systems don't bother sending a delivery-delay notice until 4 hours after the mail was sent, and I (like you, I'm sure) know of a few users in the office who notice when something takes longer than a minute to get to where it's going.
I have been known to chant:
Email is not IM
To people on occasion. Such as managers, when asked to find out why a slow delivery happened for a Grand High Manager.
Since you're on Exchange, I'm betting you want a system that'll mark the message arrived when it lands in the user's MAPI mailbox and makes Outlook go Bing.
I personally don't know of such a system off-the-shelf, but one can be written if you wish. Microsoft makes no secret about how to interface with Exchange via .NET code, and it would be pretty easy to write something to send a message via one of the Freemailers out there once every 15 minutes or so and see when it arrives.
But that only checks the mail path between the freemailer and you. Mail delays happen at the source, i.e. out of your control, much more often than internally. And that, unfortunately, can't be monitored for effectively. If your goal is to provide a chart to get a manager off your back, then that's a victory condition. But if you're looking for an honest metric of mail delivery times to your mail system, I'm afraid you're out of luck.