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Supported lipid bilayers (SLBs) at surfaces provide a route to quantitatively study molecular interactions with and at lipid membranes via different surface-based analytical techniques. Here, a method to fabricate SLBs with controlled curvatures, in the nanometer regime over large areas, is presented, utilizing lipid vesicle rupture onto nanostructured sensor substrates. Heat treated colloidal particle masks were used as templates to produce silicon dioxide films with systematically varied radius of curvature (ROC, 70 to 170 nm are demonstrated) and quartz crystal microbalance with dissipation monitoring (QCM-D) was used to confirm vesicle rupture onto such structured surfaces. Fluorescence microscopy was used to show fluidity of the supported membranes. The formation of confluent SLBs is demonstrated at the nanostructured surfaces from vesicles composed of POPC lipids. However, at surfaces with decreasing ROCs, vesicle rupture was hindered but with an increasing fraction of the positively charged lipid POEPC in the vesicles, it was possible to form good quality supported bilayers on all curvatures studied. Curved SLBs open up the possibility to systematically study the influence of curvature on molecular interactions at lipid membranes.