How can we synthesize a safe and near-optimal control policy for a partially-observed system, if all we are given is one historical input/output trajectory that has been corrupted by noise? To address this challenge, we suggest a novel data-driven controller synthesis method, that exploits recent results in controller parametrizations for partially-observed systems and analysis tools from robust control. We provide safety certificates for the learned control policy. Furthermore, the suboptimality of the proposed method shrinks to 0 - and linearly so - in terms of the model mismatch incurred during a preliminary system identification phase.