  We study a model of \textit{pinned} bilayer Wigner crystals (WC) and focus on
the effects of interlayer coherence (IC) on pinning. We consider both a
pseudospin ferromagnetic WC (FMWC) with IC and a pseudospin antiferromagnetic
WC (AFMWC) without IC. Our central finding is that a FMWC can be pinned more
strongly due to the presence of IC. One specific mechanism is through the
disorder induced interlayer tunneling, which effectively manifests as an extra
pinning in a FMWC. We also construct a general "effective disorder" model and
effective pinning Hamiltonian for the case of FMWC and AFMWC respectively.
Under this framework, pinning in the presence of IC involves
\textit{interlayer} spatial correlation of disorder in addition to intralayer
correlation, leading to \textit{enhanced} pinning in the FMWC. The pinning mode
frequency (\wpk) of a FMWC is found to decease with the effective layer
separation, whereas for an AFMWC the opposite behavior is expected. An abrupt
drop of \wpk is predicted at a transition from a FMWC to AFMWC. Possible
effects of in-plane magnetic fields and finite temperatures are addressed.
Finally we discuss some other possible ramifications of the FMWC as an
electronic supersolid-like phase.
