One fix is to not directly send the users to the result page. Instead link to a redirect script on the ddg servers i.e, duckduckgo.com/goto.php?link=http://search-result.com/ and then have goto.php remove the REFERER from the request headers.
Not sure if that will work in all browsers, iirc a 301 or a 302 can still pass those headers on. The only trick I know of that will not do that is by using a 'meta refresh' with a time set to '0', but that has bad implications for the working of the 'back' button.
Referer is a header the browser sends, Location is a header the server sends. Also, the Location header needs either a relative url on the local machine or a fully qualified one. In this case it would have needed a fully qualified one.
