Authenticated teleportation aims to certify the transmission of a quantum state through teleportation, even in the presence of an adversary. This scenario can be pictured in terms of an untrusted source distributing a Bell state between two parties who wish to verify it using some simple tests. We propose a protocol that achieves this goal in a practical way, and analyse its performance and security when the parties have noisy measurement devices. Further, we model a realistic experimental scenario where the state is subject to noise and dephasing. We finally apply our analysis to the verification of graph states with noisy measurement devices.