What’s the proper way to set the Location header for an HTTP 201 response in a Java Servlet application

Just send the absolute path. The restriction to an absolute URI is a known defect in RFC 2616 and will be fixed in HTTPbis (see http://trac.tools.ietf.org/wg/httpbis/trac/ticket/185).

Please note that RFC 7231 now includes relative URIs in the spec. See other answers for how to handle relative URIs.