  We investigate the interactions between the Legendrian satellite construction
and the existence of exact, orientable Lagrangian cobordisms between Legendrian
knots. Given Lagrangian cobordisms between two Legendrian knots and between two
Legendrian tangles, we construct a Lagrangian cobordism between Legendrian
satellites of the knots by the closures of the tangles, with extra twists on
both the top and the bottom satellite to compensate for the genus of the
cobordism. If the original cobordisms were decomposable, then a decomposable
cobordism between satellites exists as well, again with extra twists.
