<p>The emergence of quantum devices has raised a significant issue: how to certify the quantum properties of a device without placing trust in it? To characterize quantum states and measurements in a device-independent way, up to some degree of freedom, we can make use of a technique known as self-testing. Although schemes have been proposed to self-test all pure multipartite entangled states (up to complex conjugation) and real local projective measurements, little has been done to certify mixed entangled states, composite or non-projective measurements. By using the framework of quantum networks, we propose a scheme for self-testing (up to complex conjugation) arbitrary extremal measurements, including the projective ones. This then allows us to propose an indirect way to self-test any quantum state, including mixed ones, as well as any quantum measurement, including non-extremal ones. The quantum network considered here is the simple star network, which is implementable using current technologies. For our purposes, we also construct a scheme that can be used to self-test the two-dimensional tomographically complete set of measurements with an arbitrary number of parties.</p>