diff --git a/integrationtests/self/handshake_test.go b/integrationtests/self/handshake_test.go
index c6dbbfc6..741b6f31 100644
--- a/integrationtests/self/handshake_test.go
+++ b/integrationtests/self/handshake_test.go
@@ -24,12 +24,14 @@ var _ = Describe("Handshake tests", func() {
 		server        quic.Listener
 		serverConfig  *quic.Config
 		acceptStopped chan struct{}
+		tlsServerConf *tls.Config
 	)
 
 	BeforeEach(func() {
 		server = nil
 		acceptStopped = make(chan struct{})
 		serverConfig = &quic.Config{}
+		tlsServerConf = testdata.GetTLSConfig()
 	})
 
 	AfterEach(func() {
@@ -42,7 +44,7 @@ var _ = Describe("Handshake tests", func() {
 	runServer := func() quic.Listener {
 		var err error
 		// start the server
-		server, err = quic.ListenAddr("localhost:0", testdata.GetTLSConfig(), serverConfig)
+		server, err = quic.ListenAddr("localhost:0", tlsServerConf, serverConfig)
 		Expect(err).ToNot(HaveOccurred())
 
 		go func() {
@@ -117,8 +119,11 @@ var _ = Describe("Handshake tests", func() {
 					}
 				})
 
-				It("accepts the certificate", func() {
+				JustBeforeEach(func() {
 					runServer()
+				})
+
+				It("accepts the certificate", func() {
 					_, err := quic.DialAddr(
 						fmt.Sprintf("localhost:%d", server.Addr().(*net.UDPAddr).Port),
 						tlsConf,
@@ -128,17 +133,34 @@ var _ = Describe("Handshake tests", func() {
 				})
 
 				It("errors if the server name doesn't match", func() {
-					runServer()
 					_, err := quic.DialAddr(
 						fmt.Sprintf("127.0.0.1:%d", server.Addr().(*net.UDPAddr).Port),
 						tlsConf,
 						clientConfig,
 					)
+					// TODO: check the error returned locally here
 					Expect(err).To(HaveOccurred())
 				})
 
+				It("fails the handshake if the client fails to provide the requested client cert", func() {
+					tlsServerConf.ClientAuth = tls.RequireAndVerifyClientCert
+					sess, err := quic.DialAddr(
+						fmt.Sprintf("localhost:%d", server.Addr().(*net.UDPAddr).Port),
+						tlsConf,
+						clientConfig,
+					)
+					Expect(err).ToNot(HaveOccurred())
+					// The error will occur after the client already finished the handshake.
+					errChan := make(chan error)
+					go func() {
+						defer GinkgoRecover()
+						_, err := sess.AcceptStream()
+						errChan <- err
+					}()
+					Eventually(errChan).Should(Receive(MatchError("CRYPTO_ERROR: tls: bad certificate")))
+				})
+
 				It("uses the ServerName in the tls.Config", func() {
-					runServer()
 					tlsConf.ServerName = "localhost"
 					_, err := quic.DialAddr(
 						fmt.Sprintf("127.0.0.1:%d", server.Addr().(*net.UDPAddr).Port),
diff --git a/internal/handshake/crypto_setup.go b/internal/handshake/crypto_setup.go
index 5015164a..2c90089e 100644
--- a/internal/handshake/crypto_setup.go
+++ b/internal/handshake/crypto_setup.go
@@ -8,6 +8,7 @@ import (
 	"io"
 
 	"github.com/lucas-clemente/quic-go/internal/protocol"
+	"github.com/lucas-clemente/quic-go/internal/qerr"
 	"github.com/lucas-clemente/quic-go/internal/utils"
 	"github.com/marten-seemann/qtls"
 )
@@ -461,8 +462,7 @@ func (h *cryptoSetup) WriteRecord(p []byte) (int, error) {
 }
 
 func (h *cryptoSetup) SendAlert(alert uint8) {
-	// TODO(#1804): send the correct IETF QUIC error code
-	h.alertChan <- fmt.Errorf("TLS alert: %d", alert)
+	h.alertChan <- qerr.CryptoError(alert)
 }
 
 func (h *cryptoSetup) GetSealer() (protocol.EncryptionLevel, Sealer) {
diff --git a/internal/handshake/crypto_setup_test.go b/internal/handshake/crypto_setup_test.go
index c2390fd6..cd541a68 100644
--- a/internal/handshake/crypto_setup_test.go
+++ b/internal/handshake/crypto_setup_test.go
@@ -128,7 +128,7 @@ var _ = Describe("Crypto Setup TLS", func() {
 		go func() {
 			defer GinkgoRecover()
 			err := server.RunHandshake()
-			Expect(err).To(MatchError("TLS alert: 10"))
+			Expect(err).To(MatchError("CRYPTO_ERROR: tls: unexpected message"))
 			close(done)
 		}()