High-heels for biking.

At first, it seems stupid, but:

The Merrell design team includes cyclists from Montreal, one of the early bike-share cities. One of their epiphanies was that high heels are built like cycling shoes. Flexibility diminishes pedaling power, Mr. Throne said. “So for all practical purposes, the best shoe that you can have from a commuter standpoint is a woman’s heel. It’s stiff from heel to toe.”

Here's an example of the shoes in the Evera line, designed for women biking to work. It's not going to satisfy women who want to look really chic, but it would be perfectly fine for teaching a law school class and other kinds of indoor work where you're sort of dressed up, but not amongst very judgmental people.