How to test Angular2's router.navigate?

I could mock the router and make my own navigate function, but then what's the point of RouterTestingModule? Perhaps you even want to check that navigation worked.

There's no real point. If his is just a unit test for the auth guard, then just mock and spy on the mock to check that it's navigate method was called with the login argument

let router = {
  navigate: jasmine.createSpy('navigate')
}

{ provide: Router, useValue: router }

expect(authGuardService.canActivate(<any>{}, <any>{})).toBe(false);
expect(router.navigate).toHaveBeenCalledWith(['/login']);

This is how unit tests should normally be written. To try to test any actual real navigation, that would probably fall under the umbrella of end-to-end testing.

If you want to test the router without mocking it you can just inject it into your test and then spy directly on the navigate method there. The .and.stub() will make it so the call doesn't do anything.

describe('something that navigates', () => {
    it('should navigate', inject([Router], (router: Router) => {
      spyOn(router, 'navigate').and.stub();
      expect(authGuardService.canActivate(<any>{}, <any>{})).toBe(false);
      expect(router.navigate).toHaveBeenCalledWith(['/login']);
    }));
  });

this worked for me

describe('navigateExample', () => {
    it('navigate Example', () => {
        const routerstub: Router = TestBed.get(Router);
        spyOn(routerstub, 'navigate');
        component.navigateExample();
    });
});