diff --git a/packages/util-crypto/src/hmac/sha256.spec.ts b/packages/util-crypto/src/hmac/sha256.spec.ts
new file mode 100644
index 000000000..841b26d98
--- /dev/null
+++ b/packages/util-crypto/src/hmac/sha256.spec.ts
@@ -0,0 +1,21 @@
+// Copyright 2017-2021 @polkadot/util-crypto authors & contributors
+// SPDX-License-Identifier: Apache-2.0
+
+import { stringToU8a, u8aToHex } from '@polkadot/util';
+
+import { hmacSha256 } from '.';
+
+describe('hmacSha256', (): void => {
+  it('has a known output', (): void => {
+    const key = stringToU8a('secret');
+    const data = stringToU8a('some message');
+
+    expect(
+      u8aToHex(
+        hmacSha256(key, data)
+      )
+    ).toEqual(
+      '0xf28a70b41263840e5c059a0a733336e0957efba87902aa8cca11441d4b0c96d7'
+    );
+  });
+});
diff --git a/packages/util-crypto/src/hmac/sha512.spec.ts b/packages/util-crypto/src/hmac/sha512.spec.ts
new file mode 100644
index 000000000..e97c9527e
--- /dev/null
+++ b/packages/util-crypto/src/hmac/sha512.spec.ts
@@ -0,0 +1,21 @@
+// Copyright 2017-2021 @polkadot/util-crypto authors & contributors
+// SPDX-License-Identifier: Apache-2.0
+
+import { stringToU8a, u8aToHex } from '@polkadot/util';
+
+import { hmacSha512 } from '.';
+
+describe('hmacSha512', (): void => {
+  it('has a known output', (): void => {
+    const key = stringToU8a('secret');
+    const data = stringToU8a('some message');
+
+    expect(
+      u8aToHex(
+        hmacSha512(key, data)
+      )
+    ).toEqual(
+      '0x295832e97ed77be75a9fa98029497e4a722c4b9a2f21b39d34f1befa931a39ec520fd24711d6f5c03501384ea66b83066a01a82c57a0460f8cd1f471fcce5841'
+    );
+  });
+});