The effects of the coherence of waves incident upon the two sides of a coupling between two subsystems are considered, with reference to the evaluation of the coupling power between the subsystems. These effects are due to waves travelling out from the coupling being reflected from other parts of the structure, these reflections being later incident upon the coupling. It is seen that when frequency or ensemble averaged, the net coherence effects can be very substantial. However, these effects are ignored in the normal wave description of the energy flow through a coupling, such as that used in statistical energy analysis (SEA), and are a major source of error in wave-based approaches to SEA. For two, one-dimensional subsystems, a parameter γ is identified which relates wave transmission and dissipation effects and quantifies the strength of coupling between the two subsystems. When the coupling is strong (γ < 1), transmission effects dominate and the net effects of coherence are large. When the coupling is weak (γ < 1), dissipation effects dominate, coherence effects are negligible on average and normal SEA approaches give accurate estimates of the coupling power. More general cases of coupled one- and two-dimensional subsystems are then considered. The effects of coherence and the use of this parameter as a measure of strength of coupling are discussed, with coherence effects being reduced in geometrically irregular systems.