  Self-testing protocols enable the certification of quantum systems in a
device-independent manner, i.e. without knowledge of the inner workings of the
quantum devices under test. Here, we demonstrate this high standard for
characterization routines with superconducting circuits, a prime platform for
building large-scale quantum computing systems. We first develop the missing
theory allowing for the self-testing of Pauli measurements. We then self-test
Bell pair generation and measurements at the same time, performing a complete
self-test in a system composed of two entangled superconducting circuits
operated at a separation of 30 meters. In an experiment based on 17 million
trials, we measure an average CHSH (Clauser-Horne-Shimony-Holt) S-value of
2.236. Without relying on additional assumptions on the experimental setup, we
certify an average Bell state fidelity of at least 58.9% and an average
measurement fidelity of at least 89.5% in a device-independent manner, both
with 99% confidence. This enables applications in the field of distributed
quantum computing and communication with superconducting circuits, such as
delegated quantum computing.
