How to make Jest wait for all asynchronous code to finish execution before expecting an assertion

Here's a snippet that waits until pending Promises are resolved:

const flushPromises = () => new Promise(setImmediate);

Note that setImmediate is a non-standard feature (and is not expected to become standard). But if it's sufficient for your test environment, should be a good solution. Its description:

This method is used to break up long running operations and run a callback function immediately after the browser has completed other operations such as events and display updates.

Here's roughly how to use it using async/await:

it('is an example using flushPromises', async () => {
    const wrapper = mount(<App/>);
    await flushPromises();
    wrapper.update(); // In my experience, Enzyme didn't always facilitate component updates based on state changes resulting from Promises -- hence this forced re-render

    // make assertions 
});

I used this a lot in this project if you want some working real-world examples.

I'm unaware of anything native to React to accomplish what you're looking for.

However, I was able to accomplish this in similar code by calling beforeAll()'s @done after setup was complete. See changes to your code below:

let setupComplete;
jest.mock('eternalService', () => {
    return jest.fn(() => {
        return { doSomething: jest.fn((cb) => { cb('fakeReturnValue'); setupComplete(); }) };
});
.
.
.
    beforeAll(done => {
        parent = mount(<Parent />)
        setupComplete = done;
    });
});

I've never used them, but of potential interest is Jest's runAllTicks and runAllImmediates.

I would suggest you export aThingThatReturnsAPromise() from its module or file and then import it into your test case.

Since aThingThatReturnsAPromise() returns a promise, you can make use of the asynchronous testing features of Jest. Jest will wait for your promise to resolve and then you can make your assertions.

describe('When rendering Parent', () => {
    var parent;

    beforeAll(() => {
        parent = mount(<Parent />)
    });

    it('should display Child with response of the service', () => {
        expect.assertions(1);

        return aThingThatReturnsAPromise().then( () => {
            expect(parent.html()).toMatch('fakeReturnValue');
        });
    });
});

For more info, read how Jest handles test cases with Promises in the Jest Docs here