  We derive an upper bound for the distinguishability-based non-Markovianity
measure of a two-level system and prove that for certain master equations the
exact value of the measure achieves this bound. Furthermore, we obtain an
easily calculable lower bound for the divisibility-based non-Markovianity
measure of an $n$-level system. We illustrate the calculation of these bounds
through examples, considering in detail the spin-boson model. We show that the
differences between the two measures in the spin-boson model are caused by the
drift vector that is also responsible for the non-unitality of the dynamical
map.
