We derive a geometric integration formula for the partition function o
f a classical dynamical system and use it to show that corrections to
the WKB approximation vanish for any Hamiltonian which generates confo
rmal motions of some Riemannian geometry on the phase space. This gene
ralizes previous cases where the Hamiltonian was taken as an isometry
generator. We show that this conformal symmetry is similar to the usua
l formulations of the Duistermaat-Heckman integration formula in terms
of a supersymmetric Ward identity for the dynamical system. We presen
t an explicit example of a localizable Hamiltonian system in this cont
ext and use it to demonstrate how the dynamics of such systems differ
from previous examples of the Duistermaat-Heckman theorem.