We introduce a protocol for authenticated teleportation, which can be proven secure even when the receiver does not trust their measurement devices, and is experimentally accessible. We use the technique of self-testing from the device-independent approach to quantum information, where we can characterise quantum states and measurements from the exhibited classical correlations alone. First, we derive self-testing bounds for the Bell state and Pauli $\sigma_X, \sigma_Z$ measurements, that are robust enough to be implemented in the lab. Then, we use these to determine a lower bound on the fidelity of an untested entangled state to be used for teleportation. Finally, we apply our results to propose an experimentally feasible protocol for one-sided device-independent authenticated teleportation. This can be interpreted as a first practical authentication of a quantum channel, with additional one-sided device-independence.