I've done this for years, but there were two different ways we did them.
1. For personal feedback only. Fully anonymous. Not all that scientific because I got to choose who did the 360 review. Though we were assured that the results only went to ourselves and not our managers, I was always concerned. Online based, select from fully agree to fully disagree, plus places to write comments.
2. At review time. In this case, the request came from my managers boss, not my manager himself. While I don't know if my managers boss ever shared details of the feedback, like who wrote it, I was never comfortable with this. I would be extremely uncomfortable giving it directly to my manager and would have tried my best to conveniently forget the request.