  The urgent need for reliable simulation tools to match the extreme accuracy
needed to control tailored quantum devices highlights the importance of
understanding open quantum systems and their modeling. To this end, we compare
here the commonly used Redfield and Lindblad master equations against
numerically exact results in the case of one and two resonant qubits
transversely coupled at a single point to a Drude-cut ohmic bath. All the
relevant parameters are varied over a broad range which allows us to give
detailed predictions about the validity and physically meaningful applicability
of the weak-coupling approaches. We characterize the accuracy of the
approximate approaches by comparing the maximum difference of their system
evolution superoperators with numerically exact results. After optimizing the
parameters of the approximate models to minimize the difference, we also
explore if and to what extent the weak-coupling equations can be applied at
least as phenomenological models. Optimization may lead to an accurate
reproduction of experimental data, but yet our results are important to
estimate the reliability of the extracted parameter values such as the bath
temperature. Our findings set general guidelines for the range of validity of
the usual Born-Markov master equations and indicate that they fail to
accurately describe the physics in surprisingly broad range of parameters, in
particular at low temperatures. Since quantum-technological devices operate
there their accurate modeling calls for a careful choice of methods.
