  Given two fiberwise maps f1, f2 between smooth fiber bundles over a base
manifold B, we develop techniques for calculating their Nielsen coincidence
number. In certain settings we can describe the Reidemeister set of (f1,f2) as
the orbit set of a group operation of {\pi}1(B). The size and number of orbits
captures crucial extra information. E.g. for torus bundles of arbitrary
dimensions over the circle this determines the minimum coincidence numbers of
the pair (f1,f2) completely. In particular we can decide when f1 and f2 can be
deformed away from one another or when a fiberwise selfmap can be made fixed
point free by a suitable homotopy. In two concrete examples we calculate the
minimum and Nielsen numbers for all pairs of fiberwise maps explicitly. Odd
order orbits turn out to play a special role.
