Social media platforms aspire to create online experiences where users can participate safely and equitably. However, women around the world experience widespread online harassment, including insults, stalking, aggression, threats, and non-consensual sharing of sexual photos. This article describes women's perceptions of harm associated with online harassment and preferred platform responses to that harm. We conducted a survey in 14 geographic regions around the world (N = 3,993), focusing on regions whose perspectives have been insufficiently elevated in social media governance decisions (e.g. Mongolia, Cameroon). Results show that, on average, women perceive greater harm associated with online harassment than men, especially for non-consensual image sharing. Women also prefer most platform responses compared to men, especially removing content and banning users; however, women are less favorable towards payment as a response. Addressing global gender-based violence online requires understanding how women experience online harms and how they wish for it to be addressed. This is especially important given that the people who build and govern technology are not typically those who are most likely to experience online harms.