© 2019 American Physical Society. Three-dimensional nanomagnetism is a rapidly growing field of research covering both noncollinear spin textures and curved magnetic geometries including microtubular structures. We spatially resolve the field-induced magnetization reversal of free-standing ferromagnetic microtubes utilizing multifrequency magnetic force microscopy (MFM). The microtubes are composed of Co/Pd multilayer films with perpendicular magnetic anisotropy that translates to an anisotropy with radial easy axis upon rolling-up. Simultaneously mapping the topography and the perpendicular magnetostatic force derivative, the relation between surface angle and local magnetization configuration is evaluated for a large number of locations with slopes exceeding 45 degrees. The angle-dependence of the switching field is concurrent with the Kondorsky model, i.e., the rolled-up nanomembrane behaves like a planar magnetic film with perpendicular anisotropy and a pinning dominated magnetization reversal. Additionally, we discuss methodological challenges when detecting magnetostatic force derivatives near steep surfaces.