Superconducting integrated circuit layouts are proofed against the detrimental effects of stray flux by designing and fabricating them to have one or more ground planes patterned in the x-y plane with a regular grid of low-aspect-ratio flux-trapping voids. The ground plane(s) can be globally patterned with such voids and thousands or more superconducting circuit devices and wires can thereafter be laid out so as not to intersect or come so close to the voids that the trapped flux would induce supercurrents in them, thus preventing undesirable coupling of flux into circuit elements. Sandwiching a wire layer between patterned ground planes permits wires to be laid out even closer to the voids. Voids of successively smaller maximum dimension can be concentrically stacked in pyramidal fashion in multiple ground plane layers having different superconductor transition temperatures, increasing the x-y area available for device placement and wire-up.