  We introduce Lindblad-like quantum tomography (L$\ell$QT) as a quantum
characterization technique of time-correlated noise in quantum information
processors. This approach enables the estimation of time-local master
equations, including their possible negative decay rates, by maximizing a
likelihood function subject to dynamical constraints. We discuss L$\ell$QT for
the dephasing dynamics of single qubits in detail, which allows for a neat
understanding of the importance of including multiple snapshots of the quantum
evolution in the likelihood function, and how these need to be distributed in
time depending on the noise characteristics. By a detailed comparative study
employing both frequentist and Bayesian approaches, we assess the accuracy and
precision of L$\ell$QT of a dephasing quantum dynamical map that goes beyond
the Lindblad limit, focusing on two different microscopic noise models that can
be realised in either trapped-ion or superconducting-circuit architectures. We
explore the optimization of the distribution of measurement times to minimize
the estimation errors, assessing the superiority of each learning scheme
conditioned on the degree of non-Markovinity of the noise, and setting the
stage for future experimental designs of non-Markovian quantum tomography.
