  After a short review of various ways to calculate the Maslov index appearing
in semiclassical Gutzwiller type trace formulae, we discuss a
coordinate-independent and canonically invariant formulation recently proposed
by A Sugita (2000, 2001). We give explicit formulae for its ingredients and
test them numerically for periodic orbits in several Hamiltonian systems with
mixed dynamics. We demonstrate how the Maslov indices and their ingredients can
be useful in the classification of periodic orbits in complicated bifurcation
scenarios, for instance in a novel sequence of seven orbits born out of a
tangent bifurcation in the H\'enon-Heiles system.
