Integrated photonics is a leading platform for quantum technologies including nonclassical state generation1, 2, 3, 4, demonstration of quantum computational complexity5 and secure quantum communications6. As photonic circuits grow in complexity, full quantum tomography becomes impractical, and therefore an efficient method for their characterization7, 8 is essential. Here we propose and demonstrate a fast, reliable method for reconstructing the two-photon state produced by an arbitrary quadratically nonlinear optical circuit. By establishing a rigorous correspondence between the generated quantum state and classical sum-frequency generation measurements from laser light, we overcome the limitations of previous approaches for lossy multi-mode devices9, 10. We applied this protocol to a multi-channel nonlinear waveguide network and measured a 99.28±0.31% fidelity between classical and quantum characterization. This technique enables fast and precise evaluation of nonlinear quantum photonic networks, a crucial step towards complex, large-scale, device production.