diff --git a/src/__tests__/old-act.js b/src/__tests__/old-act.js
index 5414334..bcd296e 100644
--- a/src/__tests__/old-act.js
+++ b/src/__tests__/old-act.js
@@ -100,4 +100,47 @@ test('async act recovers from sync errors', async () => {
   `);
 });
 
+test('async act can handle any sort of console.error', async () => {
+  await asyncAct(async () => {
+    console.error({ error: 'some error' });
+    await null;
+  });
+
+  expect(console.error).toHaveBeenCalledTimes(2);
+  expect(console.error.mock.calls).toMatchInlineSnapshot(`
+    Array [
+      Array [
+        Array [
+          Object {
+            "error": "some error",
+          },
+        ],
+      ],
+      Array [
+        "It looks like you're using a version of react-test-renderer that supports the \\"act\\" function, but not an awaitable version of \\"act\\" which you will need. Please upgrade to at least react-test-renderer@16.9.0 to remove this warning.",
+      ],
+    ]
+  `);
+});
+
+test('async act should not show an error when ReactTestUtils.act returns something', async () => {
+  jest.resetModules();
+  jest.mock('react-test-renderer', () => ({
+    act: () => {
+      return new Promise(resolve => {
+        console.error(
+          'Warning: The callback passed to TestRenderer.act(...) function must not return anything',
+        );
+        resolve();
+      });
+    },
+  }));
+  asyncAct = require('../act-compat').asyncAct;
+  await asyncAct(async () => {
+    await null;
+  });
+
+  expect(console.error).toHaveBeenCalledTimes(0);
+});
+
 /* eslint no-console:0 */
diff --git a/src/act-compat.js b/src/act-compat.js
index 5de7829..403fab6 100644
--- a/src/act-compat.js
+++ b/src/act-compat.js
@@ -22,12 +22,15 @@ function asyncAct(cb) {
         console.error = function error(...args) {
           /* if console.error fired *with that specific message* */
           /* istanbul ignore next */
+          const firstArgIsString = typeof args[0] === 'string';
           if (
+            firstArgIsString &&
             args[0].indexOf('Warning: Do not await the result of calling TestRenderer.act') === 0
           ) {
             // v16.8.6
             isAsyncActSupported = false;
           } else if (
+            firstArgIsString &&
             args[0].indexOf(
               'Warning: The callback passed to TestRenderer.act(...) function must not return anything',
             ) === 0