The use of electromagnetic waves to obtain coherence between widely spaced Josephson tunnel junctions is explored. A pair of coupled non-linear differential equations is developed for the case of junctions used as series elements in a microstrip transmission line. We use analysis to demonstrate the existence of oscillatory traveling waves, solitary waves, and standing waves on such a transmission line. We report simulations that demonstrate these waves, and an observation of standing waves in a real series array. It appears that substantial power at frequencies above 100 GHz may be obtained from these series arrays.