jest await expect(testSubject()).rejects.toThrow expects the rejected value to be an Error object otherwise just use `rejects.toMatch`

make-sure-to-reject-an-Error-object.js

// test subjects

const rejectsStringValue = () => Promise.reject('I rejected');

const rejectsErrorValue = () => Promise.reject(new Error('I rejected'));

// tests

describe('rejectsStringValue', () => {
  it('will throw in try/catch', async () => {
    expect.assertions(1);

    try {
      await rejectsStringValue();
    } catch (e) {
      expect(e).toBe('I rejected');
    }
  });

  it('when passing the test-subject as reference', async () => {
    await expect(rejectsStringValue).rejects.not.toThrow();
    await expect(rejectsStringValue).rejects.toMatch('I rejected');
  });

  it('when executing the test-subject in the expect', async () => {
    await expect(rejectsStringValue()).rejects.not.toThrow();
    await expect(rejectsStringValue()).rejects.toMatch('I rejected');
  });
});

describe('rejectsErrorValue', () => {
  it('will throw in try/catch', async () => {
    expect.assertions(1);

    try {
      await rejectsErrorValue();
    } catch (e) {
      expect(e).toEqual(new Error('I rejected'));
    }
  });

  it('when passing the test-subject as reference', async () => {
    await expect(rejectsErrorValue).rejects.toThrow('I rejected');
  });

  it('when executing the test-subject in the expect', async () => {
    await expect(rejectsErrorValue()).rejects.toThrow('I rejected');
  });
});