diff --git a/src/jwt-middleware.ts b/src/jwt-middleware.ts
index 76e84d189..bb4425982 100644
--- a/src/jwt-middleware.ts
+++ b/src/jwt-middleware.ts
@@ -101,6 +101,8 @@ export function middleware(): express.Handler {
     authenticate(req)
       .then((jwt) => {
         if (!jwt) {
+          // Send 401 with WWW-Authenticate header as per RFC 6750
+          res.set('WWW-Authenticate', 'Bearer');
           res.status(401).end();
           return;
         }
@@ -111,12 +113,21 @@ export function middleware(): express.Handler {
           scope = `${Constants.OAUTH_PATH}:${Constants.READWRITE}`;
         }
         if (!scopeAllowsRequest(scope, req)) {
-          res.status(401).send(`Token of role ${payload.role} used out of scope: ${scope}`);
+          // insufficient_scope error code as per RFC 6750
+          const wwwAuthenticate = `Bearer error="insufficient_scope", \
+            error_description="Token of role ${payload.role} used out of \
+            scope: ${scope}"`;
+          res.set('WWW-Authenticate', wwwAuthenticate);
+          res.status(403).end();
           return;
         }
         if (payload.role !== Constants.USER_TOKEN) {
           if (!payload.scope) {
-            res.status(400).send('Token must contain scope');
+            // invalid_request error code as per RFC 6750
+            const wwwAuthenticate = `Bearer error="invalid_request", \
+              error_description="Token must contain scope"`;
+            res.set('WWW-Authenticate', wwwAuthenticate);
+            res.status(400).end();
             return;
           }
         }
diff --git a/src/test/integration/oauth-test.ts b/src/test/integration/oauth-test.ts
index 241302bf4..a86f1aed5 100644
--- a/src/test/integration/oauth-test.ts
+++ b/src/test/integration/oauth-test.ts
@@ -162,6 +162,19 @@ describe('oauth/', function () {
     customCallbackHandler = customCallbackHandlerProvided || null;
   }
 
+  it('rejects request with no JWT', async () => {
+    setupOAuth();
+
+    // Try using the access token
+    const res = await chai
+      .request(server)
+      .get(Constants.THINGS_PATH)
+      .set('Accept', 'application/json');
+    expect(res.status).toEqual(401);
+    expect(res.header).toHaveProperty('www-authenticate');
+    expect(res.get('WWW-Authenticate')).toEqual('Bearer');
+  });
+
   it('performs simple authorization', async () => {
     setupOAuth();
 
@@ -203,7 +216,9 @@ describe('oauth/', function () {
       .get(Constants.OAUTHCLIENTS_PATH)
       .set('Accept', 'application/json')
       .set(...headerAuth(jwt));
-    expect(err.status).toEqual(401);
+    expect(err.status).toEqual(403);
+    expect(err.header).toHaveProperty('www-authenticate');
+    expect(err.get('www-authenticate')).toEqual(expect.stringContaining('insufficient_scope'));
 
     res = await chai
       .request(server)
@@ -488,7 +503,9 @@ describe('oauth/', function () {
       .delete(`${Constants.THINGS_PATH}/${TEST_THING.id}`)
       .set('Accept', 'application/json')
       .set(...headerAuth(jwt));
-    expect(err.status).toEqual(401);
+    expect(err.status).toEqual(403);
+    expect(err.header).toHaveProperty('www-authenticate');
+    expect(err.get('www-authenticate')).toEqual(expect.stringContaining('insufficient_scope'));
   });
 
   it('rejects use of authorization code as access token', async () => {
@@ -521,6 +538,8 @@ describe('oauth/', function () {
       .get(Constants.THINGS_PATH)
       .set('Accept', 'application/json')
       .set(...headerAuth(jwt));
-    expect(err.status).toEqual(401);
+    expect(err.status).toEqual(403);
+    expect(err.header).toHaveProperty('www-authenticate');
+    expect(err.get('www-authenticate')).toEqual(expect.stringContaining('insufficient_scope'));
   });
 });