A novel boundary condition for a two-dimensional finite-element method (2D-FEM) is developed to simulate accessing waveguides to planar optical junctions, This new boundary condition is based on a paraxial approximation to the field's derivatives over the junction's ports, The formulation is very easily adapted within the 2D-FEM framework while providing good simulation results. Two examples are provided to show the applicability and reliability of the present method: a waveguide step discontinuity and a sharp waveguide bend.1314648