We describe the design and construction of a Variable-delay Polarization Modulator (VPM) that has been built and integrated into the Hertz ground-based, submillimeter polarimeter at the SMTO on Mt. Graham in Arizona. VPMs allow polarization modulation by controlling the phase difference between two linear, orthogonal polarizations. This is accomplished by utilizing a grid-mirror pair with a controlled separation. The size of the gap between the mirror and the polarizing grid determines the amount of the phase difference. This gap must be parallel to better than 1% of the wavelength. The necessity of controlling the phase of the radiation across this device drives the two novel features of the VPM. First, a novel, kinematic, flexure is employed that passively maintains the parallelism of the mirror and the grid to 1.5 μm over a 150 mm diameter, with a 400 μm throw. A single piezoceramic actuator is used to modulate the gap, and a capacitive sensor provides position feedback for closed-loop control. Second, the VPM uses a grid flattener that highly constrains the planarity of the polarizing grid. In doing so, the phase error across the device is minimized. Engineering results from the deployment of this device in the Hertz instrument April 2006 at the Submillimeter Telescope Observatory (SMTO) in Arizona are presented.