diff --git a/src/__tests__/old-act.js b/src/__tests__/old-act.js
index fcd531b4..b3de9377 100644
--- a/src/__tests__/old-act.js
+++ b/src/__tests__/old-act.js
@@ -98,4 +98,45 @@ 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 [
+        Object {
+          "error": "some error",
+        },
+      ],
+      Array [
+        "It looks like you're using a version of react-dom that supports the \\"act\\" function, but not an awaitable version of \\"act\\" which you will need. Please upgrade to at least react-dom@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-dom/test-utils', () => ({
+    act: () => {
+      return new Promise(resolve => {
+        console.error(
+          'Warning: The callback passed to ReactTestUtils.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 dd5f1d96..d758a97c 100644
--- a/src/act-compat.js
+++ b/src/act-compat.js
@@ -28,7 +28,9 @@ 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 ReactTestUtils.act',
             ) === 0
@@ -36,6 +38,7 @@ function asyncAct(cb) {
             // v16.8.6
             isAsyncActSupported = false
           } else if (
+            firstArgIsString &&
             args[0].indexOf(
               'Warning: The callback passed to ReactTestUtils.act(...) function must not return anything',
             ) === 0