diff --git a/test/parallel/test-crypto-hash.js b/test/parallel/test-crypto-hash.js
index f55a6768900e65..4702a9a5f175df 100644
--- a/test/parallel/test-crypto-hash.js
+++ b/test/parallel/test-crypto-hash.js
@@ -154,3 +154,10 @@ common.expectsError(
     message: 'The "algorithm" argument must be of type string'
   }
 );
+
+{
+  const Hash = crypto.Hash;
+  const instance = crypto.Hash('sha256');
+  assert(instance instanceof Hash, 'Hash is expected to return a new instance' +
+                                   ' when called without `new`');
+}
diff --git a/test/parallel/test-crypto-hmac.js b/test/parallel/test-crypto-hmac.js
index 8b9473704d3032..6c2102fe23c82c 100644
--- a/test/parallel/test-crypto-hmac.js
+++ b/test/parallel/test-crypto-hmac.js
@@ -6,6 +6,30 @@ if (!common.hasCrypto)
 const assert = require('assert');
 const crypto = require('crypto');
 
+{
+  const Hmac = crypto.Hmac;
+  const instance = crypto.Hmac('sha256', 'Node');
+  assert(instance instanceof Hmac, 'Hmac is expected to return a new instance' +
+                                   ' when called without `new`');
+}
+
+common.expectsError(
+  () => crypto.createHmac(null),
+  {
+    code: 'ERR_INVALID_ARG_TYPE',
+    type: TypeError,
+    message: 'The "hmac" argument must be of type string'
+  });
+
+common.expectsError(
+  () => crypto.createHmac('sha1', null),
+  {
+    code: 'ERR_INVALID_ARG_TYPE',
+    type: TypeError,
+    message: 'The "key" argument must be one of type string, TypedArray, or ' +
+             'DataView'
+  });
+
 {
   // Test HMAC
   const actual = crypto.createHmac('sha1', 'Node')