Catherine Amirfar, with Debevoise & Plimpton.

Earlier this summer, Catherine Amirfar stepped up to the podium to face 15 somber judges at the International Court of Justice in The Hague.

The Debevoise & Plimpton partner was appearing before the UN's highest court on behalf Qatar—a notable choice of outside counsel for an Arab nation where women commonly wear abayas and cover their hair, and a wife is required by law to obey her husband.

Citizens of a country would normally have little idea who was representing them in a dispute being litigated 3,000 miles away and in a foreign language, but this case was different. Al-Jazeera broadcast the three-day proceedings live. And people in Qatar actually tuned in, turning Amirfar into a minor celebrity, even recognized in the Doha airport.