Right, the sponsor would have to check their own logs to see how much traffic came from you. In our case the ads are local, so one person saying "I heard about you on the website" is worth a million clicks. I also encourage them to offer discounts for mentioning us. Or coupons.
Our main marketing tool is the Unique Visitor count. This may include a few bots, but it gives a figure representing the general activity of the site.
Banners are fairly useless these days (though still necessary) and modern sponsors know it . Even those without ad blockers tend to just ignore them. So we do our best to try to start discussions and write articles about sponsors. Not always easy to do on an open discussion board where people will not hesitate to tell everyone exactly what they thought about things.