I know that a for a microstrip design on a piece of substrate with a ground plane then mode is quasi-TEM. But what would the mode be for a microstrip line on a piece of substrate with no ground plane? I assume the electric field can no longer go throught the substrate so would it be something like a TE mode?
It still can act as a transmission line with relative low loss (when straight). Close to the conductor you will still have both transversal E- and H-fields, at distance, it becomes complicated. Look for Goubau line or G-line.