Previous work in the development of dual finite-element methods applied to the solution of quasistatic problems has concentrated attention on transmission lines whose cross-section has well-defined dual symmetries. Many real problems of interest have either a single symmetry axis or no symmetry axis at all. It is the purpose of the paper to deal with these special cases with the stated aim of widening the scope of application of dual methods to include any coaxial simply connected Cartesian geometry. The provision of upper and lower bounds already makes the dual-potential approach extremely powerful and flexible. Examples of practical interest are chosen including coupled rectangular metallic bars in square coaxial line.