In this paper a new approach to the synthesis of coupling matrices for microwave filters is presented. The new approach represents an advance on existing direct and optimization methods for coupling matrix synthesis in that it will exhaustively discover all possible coupling matrix solutions for a network if more than one exists. This enables a selection to be made of the set of coupling values, resonator frequency offsets, parasitic coupling tolerance etc that will be best suited to the technology it is intended to realize the microwave filter with. To demonstrate the use of the method, the case of the recently - introduced 'extended box ' coupling matrix configuration is taken. The extended box is a new class of filter configuration adapted to the synthesis of asymmetric filtering characteristics of any degree. For this configuration the number of solutions to the coupling matrix synthesis problem appears to be high and offers therefore some flexibility that can be used during the design phase. We illustrate this by carrying out the synthesis process of two asymmetric filters of 8 th and 10 th degree. In the first example a ranking criterion is defined in anticipation of a dual mode realization and allows the selection of a "best" coupling matrix out of 16 possible ones. For the 10 th degree filter a new technique of approximate synthesis is presented yielding some simplifications of the practical realization of the filter as well as of its computer aided tuning phase.