In 1973 Silvester described a finite element method which combines geometrical flexibility with a partial-fraction representation of the admittance matrices of the general N-port. His method was demonstrated for a rectangular strip. However, to the authors’ knowledge the method, though seemingly very attractive, has never been demonstrated on other two-port networks or on multi-port planar microwave circuits. It has never been implemented as a user-friendly computer-aided design tool nor has there been extensive discussion of its advantages and shortcomings. This paper attempts to revive interest in Silvester’s finite element method for planar microwave N-ports by presenting new results. Frequency-dependent admittance, impedance and scattering matrices were obtained for complicated two-port planar circuits. Comparison with other methods and measurements is made where possible. The reasons why this method is not in widespread use are discussed.