One can find various mesh truncation techniques in the literature for the finite element solution of electromagnetic scattering problems. In this paper, a mesh truncation approach referred to as the three-dimensional bymoment method is considered. This approach uses two z-directed Hertz vector potentials instead of three Cartesian field components to formulate the relevant boundary conditions. The pertaining FEM field solutions are calculated by treating the scattering problem as an interior region problem. The FEM field solutions are then numerically "coupled" on a second boundary surface that is conformal to the first one and completely enclosed by it. The "coupling" procedure yields a set of expansion coefficients, with the help of which the total field solution is written as an appropriate linear combination of the interior region FEM field solutions.