We present a class of pneumatic haptic devices that use the input motion from a user to pump fluid in a closed pneumatic circuit, meaning that the pneumatic devices require no external pressure supply. The user is coupled to a pneumatic actuator in one direction such that user motion drives fluid from the coupling device to an accumulator. When released, fluid passively returns to the user coupling until a pressure equilibrium is reached. The stiffness felt by the user is changed by opening and closing a valve between the user coupling and the accumulator. We present and experimentally validate models that characterize the system in terms of the impedance felt by the user and the speed at which the coupling refills after it has been compressed, which gives a measure of the bandwidth of the system. We give two demonstrations: one where we modulate the resistance to finger bending, and another where we enable a small actuator worn on the fingertip to create button-like haptic sensations when pressed on a flat surface.