  The measurement of the Shapiro time delay in binary pulsar systems with
highly inclined orbit can be affected both by the motion of the pulsar's
companion because of the finite time it takes a photon to cross the binary, and
by the gravitational light bending if the orbit is sufficiently edge-on
relative to the line of sight. Here we calculate the effect of retardation due
to the companion's motion on various time delays in pulsar binaries, including
the Shaipro delay, the geometric lensing delay, and the lens-induced delays
associated with the pulsar rotation. Our results can be applied to systems so
highly inclined that near conjunction gravitational lensing of the pulsar
radiation by the companion becomes important (the recently discovered double
pulsar system J0737-3039 may exemplify such a system). To the leading order,
the effect of retardation is to shift all the delay curves backward in time
around the orbit conjunction, without affecting the shape and amplitude of the
curves. The time shift is of order the photon orbit crossing time, and ranges
from a second to a few minutes for the observed binary pulsar systems. In the
double pulsar system J0737-3039, the motion of the companion may also affect
the interpretation of the recent correlated interstellar scintillation
measurements. Finally, we show that lensing sets an upper limit on the
magnitude of the frame-dragging time delay caused by the companion's spin, and
makes this delay unobservable in stellar-mass binary pulsar systems.
