The activists say they want the country's top judges to declare that women's rights are violated when they die in childbirth.
Activists say a declaration favoring the women activists would shame the government into action that drastically reduces mortality among childbearing women in Uganda.
Uganda loses 16 women in childbirth daily. Most of these deaths happen in villages where bad roads and poverty make it difficult for women to reach health centers. Even when they get there, some say, the available care is poor.
The groups presented the big to the Supreme Court on Tuesday.