Aqui está a chamada para oPUT método na minha API da Web - a terceira linha do método (estou chamando a API da Web de um front end do ASP.NET MVC):

client.BaseAddress éhttp://localhost/CallCOPAPI/.

AquicontactUri:

AquicontactUri.PathAndQuery:

E finalmente, aqui está a minha resposta 405:

Aqui está o WebApi.config no meu projeto da API da Web:

        public static void Register(HttpConfiguration config)
        {
            config.Routes.MapHttpRoute(
                name: "DefaultApi",
                routeTemplate: "api/{controller}/{id}",
                defaults: new { id = RouteParameter.Optional }
            );

            config.Routes.MapHttpRoute(
                name: "DefaultApiGet",
                routeTemplate: "api/{controller}/{action}/{regionId}",
                defaults: new { action = "Get" },
                constraints: new { httpMethod = new HttpMethodConstraint("GET") });

            var json = config.Formatters.JsonFormatter;
            json.SerializerSettings.PreserveReferencesHandling = Newtonsoft.Json.PreserveReferencesHandling.Objects;
            config.Formatters.Remove(config.Formatters.XmlFormatter);

Eu tentei desmontar o caminho que é passado paraPutAsJsonAsync parastring.Format("/api/department/{0}", department.Id) estring.Format("http://localhost/CallCOPAPI/api/department/{0}", department.Id) sem sorte.

Alguém tem alguma idéia porque estou recebendo o erro 405?

ATUALIZAR

Conforme o pedido, aqui está o código do meu controlador de departamento (vou postar tanto o código do controlador de departamento para o meu projeto de front-end, quanto o código do ApiController do departamento para o WebAPI):

Controlador do Departamento de Front-End

namespace CallCOP.Controllers
{
    public class DepartmentController : Controller
    {
        HttpClient client = new HttpClient();
        HttpResponseMessage response = new HttpResponseMessage();
        Uri contactUri = null;

        public DepartmentController()
        {
            // set base address of WebAPI depending on your current environment
            client.BaseAddress = new Uri(ConfigurationManager.AppSettings[string.Format("APIEnvBaseAddress-{0}", CallCOP.Helpers.ConfigHelper.COPApplEnv)]);

            // Add an Accept header for JSON format.
            client.DefaultRequestHeaders.Accept.Add(
                new MediaTypeWithQualityHeaderValue("application/json"));
        }

        // need to only get departments that correspond to a Contact ID.
        // GET: /Department/?regionId={0}
        public ActionResult Index(int regionId)
        {
            response = client.GetAsync(string.Format("api/department/GetDeptsByRegionId/{0}", regionId)).Result;
            if (response.IsSuccessStatusCode)
            {
                var departments = response.Content.ReadAsAsync<IEnumerable<Department>>().Result;
                return View(departments);
            }
            else
            {
                LoggerHelper.GetLogger().InsertError(new Exception(string.Format(
                    "Cannot retrieve the list of department records due to HTTP Response Status Code not being successful: {0}", response.StatusCode)));
                return RedirectToAction("Index");
            }

        }

        //
        // GET: /Department/Create

        public ActionResult Create(int regionId)
        {
            return View();
        }

        //
        // POST: /Department/Create
        [HttpPost]
        [ValidateAntiForgeryToken]
        public ActionResult Create(int regionId, Department department)
        {
            department.RegionId = regionId;
            response = client.PostAsJsonAsync("api/department", department).Result;
            if (response.IsSuccessStatusCode)
            {
                return RedirectToAction("Edit", "Region", new { id = regionId });
            }
            else
            {
                LoggerHelper.GetLogger().InsertError(new Exception(string.Format(
                    "Cannot create a new department due to HTTP Response Status Code not being successful: {0}", response.StatusCode)));
                return RedirectToAction("Edit", "Region", new { id = regionId });
            }
        }

        //
        // GET: /Department/Edit/5

        public ActionResult Edit(int id = 0)
        {
            response = client.GetAsync(string.Format("api/department/{0}", id)).Result;
            Department department = response.Content.ReadAsAsync<Department>().Result;
            if (department == null)
            {
                return HttpNotFound();
            }
            return View(department);
        }

        //
        // POST: /Department/Edit/5

        [HttpPost]
        [ValidateAntiForgeryToken]
        public ActionResult Edit(int regionId, Department department)
        {
            response = client.GetAsync(string.Format("api/department/{0}", department.Id)).Result;
            contactUri = response.RequestMessage.RequestUri;
            response = client.PutAsJsonAsync(string.Format(contactUri.PathAndQuery), department).Result;
            if (response.IsSuccessStatusCode)
            {
                return RedirectToAction("Index", new { regionId = regionId });
            }
            else
            {
                LoggerHelper.GetLogger().InsertError(new Exception(string.Format(
                    "Cannot edit the department record due to HTTP Response Status Code not being successful: {0}", response.StatusCode)));
                return RedirectToAction("Index", new { regionId = regionId });
            }
        }

        //
        // GET: /Department/Delete/5

        public ActionResult Delete(int id = 0)
        {
            response = client.GetAsync(string.Format("api/department/{0}", id)).Result;
            Department department = response.Content.ReadAsAsync<Department>().Result;

            if (department == null)
            {
                return HttpNotFound();
            }
            return View(department);
        }

        //
        // POST: /Department/Delete/5

        [HttpPost, ActionName("Delete")]
        [ValidateAntiForgeryToken]
        public ActionResult DeleteConfirmed(int regionId, int id)
        {
            response = client.GetAsync(string.Format("api/department/{0}", id)).Result;
            contactUri = response.RequestMessage.RequestUri;
            response = client.DeleteAsync(contactUri).Result;
            return RedirectToAction("Index", new { regionId = regionId });
        }
    }
}

Departamento de APIs da Web ApiController

namespace CallCOPAPI.Controllers
{
    public class DepartmentController : ApiController
    {
        private CallCOPEntities db = new CallCOPEntities(HelperClasses.DBHelper.GetConnectionString());

        // GET api/department
        public IEnumerable<Department> Get()
        {
            return db.Departments.AsEnumerable();
        }

        // GET api/department/5
        public Department Get(int id)
        {
            Department dept = db.Departments.Find(id);
            if (dept == null)
            {
                throw new HttpResponseException(Request.CreateResponse(HttpStatusCode.NotFound));
            }

            return dept;
        }

        // this should accept a contact id and return departments related to the particular contact record
        // GET api/department/5
        public IEnumerable<Department> GetDeptsByRegionId(int regionId)
        {
            IEnumerable<Department> depts = (from i in db.Departments
                                             where i.RegionId == regionId 
                                             select i);
            return depts;
        }

        // POST api/department
        public HttpResponseMessage Post(Department department)
        {
            if (ModelState.IsValid)
            {
                db.Departments.Add(department);
                db.SaveChanges();

                HttpResponseMessage response = Request.CreateResponse(HttpStatusCode.Created, department);
                return response;
            }
            else
            {
                return Request.CreateErrorResponse(HttpStatusCode.BadRequest, ModelState);
            }
        }

        // PUT api/department/5
        public HttpResponseMessage Put(int id, Department department)
        {
            if (!ModelState.IsValid)
            {
                return Request.CreateErrorResponse(HttpStatusCode.BadRequest, ModelState);
            }

            if (id != department.Id)
            {
                return Request.CreateResponse(HttpStatusCode.BadRequest);
            }

            db.Entry(department).State = EntityState.Modified;

            try
            {
                db.SaveChanges();
            }
            catch (DbUpdateConcurrencyException ex)
            {
                return Request.CreateErrorResponse(HttpStatusCode.NotFound, ex);
            }

            return Request.CreateResponse(HttpStatusCode.OK);
        }

        // DELETE api/department/5
        public HttpResponseMessage Delete(int id)
        {
            Department department = db.Departments.Find(id);
            if (department == null)
            {
                return Request.CreateResponse(HttpStatusCode.NotFound);
            }

            db.Departments.Remove(department);

            try
            {
                db.SaveChanges();
            }
            catch (DbUpdateConcurrencyException ex)
            {
                return Request.CreateErrorResponse(HttpStatusCode.NotFound, ex);
            }

            return Request.CreateResponse(HttpStatusCode.OK, department);
        }
    }
}