  We present two complementary strategies for modeling nonlinear quantum optics
in realistic integrated optical devices, where scattering loss is present. In
the first strategy, we model scattering loss as an attenuation; in the second,
we employ a Hamiltonian treatment that includes a mechanism for scattering
loss, such as a `phantom waveguide.' These strategies can be applied to a broad
range of structures and processes. As an example, we use these two approaches
to model spontaneous four-wave mixing in (i) a ring-channel system and (ii) an
add-drop system. Even for these well-understood systems, our strategies yield
some novel results. We show the rates of photon pairs, broken pairs, and lost
pairs and their dependence on system parameters. We show that the properties of
lost and broken photon pairs in such structures can be related to those of the
un-scattered photon pairs, which are relatively simple to measure.
