  The problem of building coherent states from non-normalizable fiducial states
is considered. We propose a way of constructing such coherent states by
regularizing the divergence of the fiducial state norm. Then, we successfully
apply the formalism to particular cases involving systems with a continuous
spectrum: coherent states for the free particle and for the inverted oscillator
$(p^2 - x^2)$ are explicitly provided. Similar ideas can be used for other
systems having non-normalizable fiducial states.
