Thanks, I figured it out:
String xml = given().request().header("SOAPAction","authenticate")
.contentType("application/soap+xml; charset=UTF-8;").body(myEnvelope).when()
.post( "/myserviceuri/mynamedport" ).andReturn().asString();
I needed to pass the SOAPAction header (defined in the WSDL) in order to do it.
-Jon