  In order to provide a guaranteed precision and a more accurate judgement
about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an
upper bound (equivalently a lower bound on the quantum Fisher information) for
precision of estimation is introduced. Unlike the bounds previously introduced
in the literature, the upper bound is saturable and yields a practical
instruction to estimate the parameter through preparing the optimal initial
state and optimal measurement. The bound is based on the underling dynamics and
its calculation is straightforward and requires only the matrix representation
of the quantum maps responsible for encoding the parameter. This allows us to
apply the bound to open quantum systems whose dynamics are described by either
semigroup or non-semigroup maps. Reliability and efficiency of the method to
predict the ultimate precision limit are demonstrated by {three} main examples.
