Electronic devices can be provided with at least one first circuit component coupled to a first circuit board, at least one second circuit component coupled to a second circuit board, and a mating assembly coupled to the boards for holding them in a vertical stack. The first circuit components can face the second circuit components in the stack. One or more of the first circuit components can be horizontally offset from one or more of the second circuit components in the stack to reduce the thickness of the mated circuit boards. Portions of the circuit boards and the mating assembly can shield the circuit components of the stack from electromagnetic interference.