Efforts to cure human immunodeficiency virus (HIV) infection are obstructed by reservoirs of latently infected CD4 T cells that can reestablish viremia. HIV-specific broadly neutralizing antibodies (bNAbs), defined by unusually wide neutralization breadths against globally diverse viruses, may contribute to the elimination of these reservoirs by binding to reactivated cells, thus targeting them for immune clearance. However, the relationship between neutralization of reservoir isolates and binding to corresponding infected primary CD4 T cells has not been determined. Thus, the extent to which neutralization breadths and potencies can be used to infer the corresponding parameters of infected cell binding is currently unknown. We assessed the breadths and potencies of bNAbs against 36 viruses reactivated from peripheral blood CD4 T cells from antiretroviral (ARV)-treated HIV-infected individuals by using paired neutralization and infected cell binding assays. Single-antibody breadths ranged from 0 to 64% for neutralization (80% inhibitory concentration [IC] of ≤10 μg/ml) and from 0 to 89% for binding, with two-antibody combinations (results for antibody combinations are theoretical/predicted) reaching levels of 0 to 83% and 50 to 100%, respectively. Infected cell binding correlated with virus neutralization for 10 of 14 antibodies (e.g., for 3BNC117, = 0.82 and < 0.0001). Heterogeneity was observed, however, with a lack of significant correlation for 2G12, CAP256.VRC26.25, 2F5, and 4E10. Our results provide guidance on the selection of bNAbs for interventional cure studies, both by providing a direct assessment of intra- and interindividual variabilities in neutralization and infected cell binding in a novel cohort and by defining the relationships between these parameters for a panel of bNAbs. Although antiretroviral therapies have improved the lives of people who are living with HIV, they do not cure infection. Efforts are being directed towards harnessing the immune system to eliminate the virus that persists, potentially resulting in virus-free remission without medication. HIV-specific antibodies hold promise for such therapies owing to their ability to both prevent the infection of new cells (neutralization) and direct the killing of infected cells. We isolated 36 HIV strains from individuals whose virus was suppressed by medication and tested 14 different antibodies for neutralization of these viruses and for binding to cells infected with the same viruses (critical for engaging natural killer cells). For both neutralization and infected cell binding, we observed variation both between individuals and amongst different viruses within an individual. For most antibodies, neutralization activity correlated with infected cell binding. These data provide guidance on the selection of antibodies for clinical trials.