This paper presents a method of designing bandpass and band-rejection microwave filters by appropriately transforming lumped-element filters. Such microwave filters are realized physically as chains of resonant elements (either cavities or irises), coupled by quarter-wave sections of line. A structure of this type has a number of practical advantages over other types of filter structures, such as a chain of directly coupled cavities, because it permits the construction of the resonant elements as separate units, and yields more liberal tolerances on the dimensions of the coupling irises. A comparison is made of the theoretical and measured characteristics of an experimental four-cavity filter.