diff --git a/changelog/unreleased/issue-376 b/changelog/unreleased/issue-376
new file mode 100644
index 0000000..eca3bdd
--- /dev/null
+++ b/changelog/unreleased/issue-376
@@ -0,0 +1,7 @@
+Bugfix: Include a Basic authentication challenge when credentials are rejected
+
+Requests rejected by Basic authentication now include a `WWW-Authenticate` header,
+allowing HTTP clients to prompt for credentials.
+
+https://github.com/restic/rest-server/issues/376
+https://github.com/restic/rest-server/pull/396
diff --git a/handlers.go b/handlers.go
index 5938edd..691afa8 100644
--- a/handlers.go
+++ b/handlers.go
@@ -59,7 +59,7 @@ func (s *Server) ServeHTTP(w http.ResponseWriter, r *http.Request) {
 	// First of all, check auth (will always pass if NoAuth is set)
 	username, ok := s.checkAuth(r)
 	if !ok {
-		httpDefaultError(w, http.StatusUnauthorized)
+		s.writeUnauthorized(w)
 		return
 	}
 
diff --git a/mux.go b/mux.go
index 9c604b3..a6962f4 100644
--- a/mux.go
+++ b/mux.go
@@ -56,11 +56,18 @@ func (s *Server) checkAuth(r *http.Request) (username string, ok bool) {
 	return username, true
 }
 
+func (s *Server) writeUnauthorized(w http.ResponseWriter) {
+	if !s.NoAuth && s.ProxyAuthUsername == "" {
+		w.Header().Set("WWW-Authenticate", `Basic realm="rest-server"`)
+	}
+	httpDefaultError(w, http.StatusUnauthorized)
+}
+
 func (s *Server) wrapMetricsAuth(f http.HandlerFunc) http.HandlerFunc {
 	return func(w http.ResponseWriter, r *http.Request) {
 		username, ok := s.checkAuth(r)
 		if !ok {
-			httpDefaultError(w, http.StatusUnauthorized)
+			s.writeUnauthorized(w)
 			return
 		}
 		if s.PrivateRepos && username != "metrics" {
diff --git a/mux_test.go b/mux_test.go
index 66c09b0..3558825 100644
--- a/mux_test.go
+++ b/mux_test.go
@@ -1,6 +1,7 @@
 package restserver
 
 import (
+	"net/http"
 	"net/http/httptest"
 	"testing"
 )
@@ -78,3 +79,57 @@ func TestCheckAuth(t *testing.T) {
 		})
 	}
 }
+
+func TestUnauthorizedResponsesIncludeBasicChallenge(t *testing.T) {
+	const challenge = `Basic realm="rest-server"`
+
+	tests := []struct {
+		name          string
+		server        *Server
+		metrics       bool
+		wantChallenge string
+	}{
+		{
+			name:          "server Basic authentication",
+			server:        &Server{},
+			wantChallenge: challenge,
+		},
+		{
+			name:   "server proxy authentication",
+			server: &Server{ProxyAuthUsername: "X-Remote-User"},
+		},
+		{
+			name:          "metrics Basic authentication",
+			server:        &Server{},
+			metrics:       true,
+			wantChallenge: challenge,
+		},
+		{
+			name:    "metrics proxy authentication",
+			server:  &Server{ProxyAuthUsername: "X-Remote-User"},
+			metrics: true,
+		},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			var handler http.HandlerFunc
+			if tt.metrics {
+				handler = tt.server.wrapMetricsAuth(func(http.ResponseWriter, *http.Request) {
+					t.Fatal("handler should not be called for an unauthorized request")
+				})
+			} else {
+				handler = tt.server.ServeHTTP
+			}
+
+			rec := httptest.NewRecorder()
+			handler(rec, httptest.NewRequest(http.MethodGet, "/", nil))
+			if rec.Code != http.StatusUnauthorized {
+				t.Fatalf("status = %d, want %d", rec.Code, http.StatusUnauthorized)
+			}
+			if got := rec.Header().Get("WWW-Authenticate"); got != tt.wantChallenge {
+				t.Errorf("WWW-Authenticate = %q, want %q", got, tt.wantChallenge)
+			}
+		})
+	}
+}