The invention relates to circuit boards and to screening circuits and components on such boards from stray rf interference when they are mounted as arrays or stacks of such circuit boards. The circuit boards (12, 14) are individually screened by conductive screening layers (16, 18) as known in the art and the individual screening layers are coupled together by layered interconnects (34) which connect corresponding screening layers (16, 18) of the individual circuit boards (12, 14) together, instead of by vias.