I was reading the help files of a well-known commercial microwave FEA package and it suggested calculating characteristic impedance from the power and voltage rather than finding the current directly.

This way doesn't require surface normals or line integrals which my previous methods did, so it's probably better (easier to do anyway). I've added this into my TEM mode post - https://comphysblog.wordpress.com/2018/09/06/tem-mode-analysis-with-fenics/