All quantum systems couple to their surrounding environment, itself composed of unmonitored quantum-coherent degrees of freedom. Often the environment exhibits a memory of the system’s state, resulting in Non-Markovian return of quantum information to the system at later times. Since current techniques to reconstruct a system’s state from experimental data, such as stochastic master equations (SME’s), rely on Markovianity, understanding how quantum-coherent devices evolve in the presence of non-Markovian effects remains an outstanding problem. We use continuous quantum state tracking with weak measurement to experimentally investigate non-Markovianity in transmon superconducting qubits and train recurrent neural network models to reconstruct quantum trajectories, motivated by such models’ demonstrated ability to learn long-time correlations in sequential data. Accurately reconstructed quantum trajectories in turn enable us to determine the degree to which a system is non-Markovian, estimate time-dependent SME parameters, and map heterodyne backaction.