_restFulServiceHost = new WebServiceHost(typeof(RestDemoService), new Uri(RestAddress));
      _restFulServiceHost.Open();

        var req = (HttpWebRequest)WebRequest.Create(restConfig.EndpointAddress);
        req.Method = "POST";
        ...
        return (HttpWebResponse)req.GetResponse();

        req.ClientCertificates.Add(GetMyCertificate());

      _restFulServiceHost = new ServiceHost(typeof(RestDemoService));
      _restFulServiceHost.AddServiceEndpoint(typeof(IRestDemoService), _basicHttpBinding, RestAddress);

    private readonly Binding _basicHttpBinding = new BasicHttpBinding
                                                    {
                                                      Security =
                                                        {
                                                          Mode = BasicHttpSecurityMode.TransportWithMessageCredential,
                                                          Message =
                                                            {
                                                              ClientCredentialType = BasicHttpMessageCredentialType.Certificate
                                                            }
                                                        },
                                                      Namespace = "http://mysite.com"
                                                    };

System.Net.WebException was caught
  Message=The underlying connection was closed: An unexpected error occurred on a send.
  Source=System
  StackTrace:
       at System.Net.HttpWebRequest.GetResponse()

req.ClientCertificates.Add(GetMyCertificate());

        myClient.ClientCredentials.ClientCertificate.SetCertificate(
          StoreLocation.LocalMachine,
          StoreName.My,
          X509FindType.FindBySubjectName,
          "*.mycert.com");

      _restFulServiceHost = new WebServiceHost(typeof(RestDemoService), new Uri(RestAddress));
      _restFulServiceHost.Open();

      _restFulServiceHost = new WebServiceHost(typeof(RestDemoService));
      _restFulServiceHost.AddServiceEndpoint(typeof(IRestDemoService), WebHttpBindingWithCert, RestAddressHttps); // https
      _restFulServiceHost.Open();
...
    public WebHttpBinding WebHttpBindingWithCert
    {
      get
      {
        return new WebHttpBinding
                 {
                   Security =
                     {
                       Mode = WebHttpSecurityMode.Transport,
                       Transport = {ClientCredentialType = HttpClientCredentialType.Certificate}
                     }
                 };
      }
    }

      req.ClientCertificates.Add(GetMetangaCertificate());