  Exact master equations describing the decay of a two-state system into a
structured reservoir are constructed. Employing the exact solution for the
model we determine analytical expressions for the memory kernel of the
Nakajima-Zwanzig master equation and for the generator of the corresponding
time-convolutionless master equation. This approach allows a detailed
investigation and comparison of the convergence behavior of the corresponding
perturbation expansions. Moreover, we find that the structure of widely used
phenomenological master equations with memory kernel may be incompatible with a
non-perturbative treatment of the underlying microscopic model. We discuss
several physical implications of our results on the microscopic analysis and
the phenomenological modelling of non-Markovian quantum dynamics of open
systems.
