These award sites are drawing tons of traffic to their own web site. The reason is because all the web sites who get the awards are linking right back to them by posting the award on their web site.
What is stopping you from offering other awards to other web sites? You could design a graphic for the award. The graphic could include something that will draw them to your web site. Have an online form at your web site so other people can enter to qualify for the award. You then judge all the entrees and pick a winner. You give them the award graphic with a link included. They post it on their web site and now they're linking your web site.
You could offer web site awards for many reasons. The web site might offer outstanding and original content. The design of the web site could be very
professional. It could have a fast load time. It could include original web features that aren't found on most web sites. The site may be easy to navigate through.
Let's say you give out 20 web site awards a week. In a year that would be 1040 people linking to your web site. If you received 2 hits a week from each
link, that would be 104 hits a year from each award you have given. That equals an extra 108,160 hits to your web site a year!