diff --git a/std/node/_util/_util_callbackify_test.ts b/std/node/_util/_util_callbackify_test.ts
index d6a5d86644..e8a3139053 100644
--- a/std/node/_util/_util_callbackify_test.ts
+++ b/std/node/_util/_util_callbackify_test.ts
@@ -246,7 +246,7 @@ Deno.test("callbackify passes arguments to the original", async () => {
 
   for (const value of values) {
     // eslint-disable-next-line require-await
-    async function asyncFn<T>(arg: T): Promise<T> {
+    async function asyncFn(arg: typeof value): Promise<typeof value> {
       assertStrictEquals(arg, value);
       return arg;
     }
@@ -263,7 +263,7 @@ Deno.test("callbackify passes arguments to the original", async () => {
       });
     });
 
-    function promiseFn<T>(arg: T): Promise<T> {
+    function promiseFn<T>(arg: typeof value): Promise<typeof value> {
       assertStrictEquals(arg, value);
       return Promise.resolve(arg);
     }
diff --git a/std/node/_util/_util_promisify.ts b/std/node/_util/_util_promisify.ts
index e3cc36a0c1..ea2fb6a5e3 100644
--- a/std/node/_util/_util_promisify.ts
+++ b/std/node/_util/_util_promisify.ts
@@ -21,13 +21,30 @@
 // OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
 // USE OR OTHER DEALINGS IN THE SOFTWARE.
 
+// Hack: work around the following TypeScript error:
+//   error: TS2345 [ERROR]: Argument of type 'typeof kCustomPromisifiedSymbol'
+//   is not assignable to parameter of type 'typeof kCustomPromisifiedSymbol'.
+//        assertStrictEquals(kCustomPromisifiedSymbol, promisify.custom);
+//                                                     ~~~~~~~~~~~~~~~~
+declare const _CustomPromisifiedSymbol: unique symbol;
+declare const _CustomPromisifyArgsSymbol: unique symbol;
+declare let Symbol: SymbolConstructor;
+interface SymbolConstructor {
+  for(key: "nodejs.util.promisify.custom"): typeof _CustomPromisifiedSymbol;
+  for(
+    key: "nodejs.util.promisify.customArgs"
+  ): typeof _CustomPromisifyArgsSymbol;
+}
+// End hack.
+
 // In addition to being accessible through util.promisify.custom,
-// this symbol is registered globally and can be accessed in any environment as Symbol.for('nodejs.util.promisify.custom')
+// this symbol is registered globally and can be accessed in any environment as
+// Symbol.for('nodejs.util.promisify.custom').
 const kCustomPromisifiedSymbol = Symbol.for("nodejs.util.promisify.custom");
-// This is an internal Node symbol used by functions returning multiple arguments
-// e.g. ['bytesRead', 'buffer'] for fs.read.
+// This is an internal Node symbol used by functions returning multiple
+// arguments, e.g. ['bytesRead', 'buffer'] for fs.read().
 const kCustomPromisifyArgsSymbol = Symbol.for(
-  "deno.nodejs.util.promisify.customArgs"
+  "nodejs.util.promisify.customArgs"
 );
 
 class NodeInvalidArgTypeError extends TypeError {
diff --git a/std/node/_util/_util_promisify_test.ts b/std/node/_util/_util_promisify_test.ts
index c6dbbd45a5..4369a01329 100644
--- a/std/node/_util/_util_promisify_test.ts
+++ b/std/node/_util/_util_promisify_test.ts
@@ -30,7 +30,7 @@ import { promisify } from "./_util_promisify.ts";
 import * as fs from "../fs.ts";
 
 const readFile = promisify(fs.readFile);
-const customPromisifyArgs = Symbol.for("deno.nodejs.util.promisify.customArgs");
+const customPromisifyArgs = Symbol.for("nodejs.util.promisify.customArgs");
 
 Deno.test(
   "Errors should reject the promise",
diff --git a/std/testing/asserts.ts b/std/testing/asserts.ts
index ea15aa6bc1..0cbd6d2ad5 100644
--- a/std/testing/asserts.ts
+++ b/std/testing/asserts.ts
@@ -133,7 +133,7 @@ export function equal(c: unknown, d: unknown): boolean {
   })(c, d);
 }
 
-/** Make an assertion, if not `true`, then throw. */
+/** Make an assertion, error will be thrown if `expr` does not have truthy value. */
 export function assert(expr: unknown, msg = ""): asserts expr {
   if (!expr) {
     throw new AssertionError(msg);
@@ -143,7 +143,19 @@ export function assert(expr: unknown, msg = ""): asserts expr {
 /**
  * Make an assertion that `actual` and `expected` are equal, deeply. If not
  * deeply equal, then throw.
+ *
+ * Type parameter can be specified to ensure values under comparison have the same type.
+ * For example:
+ *```ts
+ *assertEquals<number>(1, 2)
+ *```
  */
+export function assertEquals(
+  actual: unknown,
+  expected: unknown,
+  msg?: string
+): void;
+export function assertEquals<T>(actual: T, expected: T, msg?: string): void;
 export function assertEquals(
   actual: unknown,
   expected: unknown,
@@ -174,7 +186,19 @@ export function assertEquals(
 /**
  * Make an assertion that `actual` and `expected` are not equal, deeply.
  * If not then throw.
+ *
+ * Type parameter can be specified to ensure values under comparison have the same type.
+ * For example:
+ *```ts
+ *assertNotEquals<number>(1, 2)
+ *```
  */
+export function assertNotEquals(
+  actual: unknown,
+  expected: unknown,
+  msg?: string
+): void;
+export function assertNotEquals<T>(actual: T, expected: T, msg?: string): void;
 export function assertNotEquals(
   actual: unknown,
   expected: unknown,
@@ -204,10 +228,13 @@ export function assertNotEquals(
 /**
  * Make an assertion that `actual` and `expected` are strictly equal.  If
  * not then throw.
+ * ```ts
+ * assertStrictEquals(1, 2)
+ * ```
  */
-export function assertStrictEquals(
-  actual: unknown,
-  expected: unknown,
+export function assertStrictEquals<T>(
+  actual: T,
+  expected: T,
   msg?: string
 ): void {
   if (actual === expected) {
@@ -265,9 +292,25 @@ export function assertStringContains(
 }
 
 /**
- * Make an assertion that `actual` contains the `expected` values
- * If not then thrown.
+ * Make an assertion that `actual` contains the `expected` values.
+ * If not then an error will be thrown.
+ *
+ * Type parameter can be specified to ensure values under comparison have the same type.
+ * For example:
+ *```ts
+ *assertArrayContains<number>([1, 2], [2])
+ *```
  */
+export function assertArrayContains(
+  actual: ArrayLike<unknown>,
+  expected: ArrayLike<unknown>,
+  msg?: string
+): void;
+export function assertArrayContains<T>(
+  actual: ArrayLike<T>,
+  expected: ArrayLike<T>,
+  msg?: string
+): void;
 export function assertArrayContains(
   actual: ArrayLike<unknown>,
   expected: ArrayLike<unknown>,
diff --git a/std/testing/asserts_test.ts b/std/testing/asserts_test.ts
index 5537b41e79..854cb97304 100644
--- a/std/testing/asserts_test.ts
+++ b/std/testing/asserts_test.ts
@@ -412,6 +412,17 @@ Deno.test({
   },
 });
 
+Deno.test({
+  name: "assert* functions with specified type paratemeter",
+  fn(): void {
+    assertEquals<string>("hello", "hello");
+    assertNotEquals<number>(1, 2);
+    assertArrayContains<boolean>([true, false], [true]);
+    const value = { x: 1 };
+    assertStrictEquals<typeof value>(value, value);
+  },
+});
+
 Deno.test("Assert Throws Non-Error Fail", () => {
   assertThrows(
     () => {