Recent advances in membrane biophysics have driven deeper investigations into lipid bilayer asymmetry and its biological implications. Molecular dynamics simulations of asymmetric membranes have recently highlighted the potential role of differential stress in regulating membrane elastic moduli and phase behavior, in addition to the already known composition asymmetries. The vast majority of MD simulations of membranes are flat, tensionless, fully periodic geometries, which artificially suppress membrane bending even in the presence of a non-vanishing net torque. In order to allow a membrane to relax to its true equilibrium curvature state determined by a sensitive balance of monolayer area strains and spontaneous curvatures, it is desirable to simulate with periodicity in only one direction with open edges along the other. However, lipid flip-flop over the open edges rapidly destroys any membrane asymmetry. We present a technique for maintaining membrane asymmetry with open edges by applying “sticky tape” to the membrane edges parallel to the direction of periodicity to prevent flip-flop. By varying lipid number asymmetry at fixed monolayer compositions, this free-curvature technique can be used to determine the voluntarily flat state of an asymmetric membrane, which can be transferred to fully periodic conditions for production. By monitoring membrane curvature as a function of number asymmetry in composition-symmetric systems, monolayer spontaneous curvatures can be deduced without the need to calculate lateral stress profiles and relate their moments to continuum theory. Importantly, this method does not significantly impact the structure of the fluid lipid phase in the bulk. We present this technique using the ultra-coarse-grained Cooke lipid model, but the concept is easily transferable to more finely-resolved models, allowing for simultaneously area- and curvature-relaxed membrane simulations.