Microphone assemblies may be provided that have microelectromechanical systems microphones and associated application-specific integrated circuits mounted to printed circuit boards. The application-specific integrated circuits may contain amplifier circuitry for amplifying microphone signals from the microphone. One or more though-silicon vias may be formed in the application-specific integrated circuit that serve as an acoustic port through which sound may pass. The application-specific integrated circuit may be embedded in the printed circuit board and the microphone may be mounted to the upper surface of the printed circuit board, the application-specific integrated circuit and microphone may be stacked on the upper surface of the printed circuit board, or the microphone and application-specific integrated circuit may be mounted to the printed circuit board so that the microphone is received within an opening in the printed circuit board.