Meaza served as a Judge of the High Court of Ethiopia between 1989 and 1992. In 1993 she was appointed by the Ethiopian Constitution Commission as a legal adviser. In 1995, Meaza founded the Ethiopian Women Lawyers Association, and became its executive director. Through her legal contacts, she has been instrumental in campaigning for women's rights in Ethiopia; her Fighting For Women's Rights In Ethiopia group had approximately 45 graduate lawyers working for it in 2002. Meaza has held a position with the United Nations Economic Commission for Africa. She helped lead the development of the first women's bank in Ethiopia, Enat Bank, which was established in 2011 and as of 2016 chairs its board of directors.
Political positions
In a 2009 speech Meaza was outspoken on the stereotypes that women face in Ethiopian society, blaming Amharic proverbs for the way women are perceived, portraying them mostly as delicate and weak. The communications tradition over time has used these proverbs to advance men and degrade women. Some of the ideas given by these proverbs are that a woman's place is only in domestic duties and that women in general lack common sense and are irresponsible. One of these Amharic proverbs that Meaza is alluding to says that a woman can not to be trusted and another conveys the idea that the companionship of a woman is dispersed by a mouse. Another proverb indicates that even if a woman is smart, only a man can be practical to apply knowledge – hinting at gender based roles in urban Ethiopian society, especially in Addis Ababa. Still another of the proverbs she alludes to is of emotional characteristics where the proverb speaks of the courage of a woman as about as useless as a shy priest or a blind donkey.
Recognition
Meaza has received numerous awards for philanthropy and leadership, including the African Leadership Prize; and is an active member of several women's rights advocacy organizations. In 2003, she became a Hunger Project Award laureate, winning the Grassroots Ethiopian Women of Substance Africa Prize, Two years later, she was nominated for the Nobel Peace Prize. Her most famous case was turned into the 2014 Ethiopian film Difret, which was promoted by Angelina Jolie as executive producer and went on to win the World Cinematic Dramatic Audience Award at the 2014 Sundance Film Festival.