Continuity Conditions at a General Wave Boundary:

is there some general approach to deducing the continuity conditions at a wave boundary for any type of wave – quantum, string, pressure etc. that works for you in your physics. I find it difficult to just see what should be continuous and what can afford to be discontinuous. An example might be Conservation of Momentum and Energy – do these laws always (relatively) straightforwardly lead to the continuity conditions or is there some better way?