In my area the universities and schools set up a program where they reach out to local companies who can volunteer to be involved. So the students would then perform web design services for them as part of their school projects. It takes awhile to get it started and get the word out, but after a year or two people will learn about it and it's easier to find companies to help.
At my university our senior year we had to do a full project front to back for a real company. Not all projects are actually used by the companies - just depends on how good it was :]
OR you could make it an entrepreneurial project as well and have the student each find prospects and then they would have to sell the startup on allowing them to do their design. It could still be for free, but that isn't necessarily an easy sell. Give them some experience getting in touch with people, and discussing services and needs.
Ask them! I know a handful of startups who would love to work with new designers on thinking through simple UX facelifts, and these would be an appropriate amount of work for a single quarter of a University class.