A high contrast is required for direct imaging of exoplanets. Ideally, the level of contrast required for direct imaging of exoplanets can be achieved by coronagraphic imaging, but in practice, the contrast is degraded by wavefront aberrations. To achieve the required contrast, low-order wavefront aberrations such as tip-tilt, defocus and coma must be determined and corrected. In this paper, we present a technique that integrates a sparse-aperture mask (SAM) with a shaped pupil coronagraph (SPC) to make precise estimates of these low-order aberrations. Starlight rejected by the coronagraph's focal plane stop is collimated to a relay pupil, where the mask forms an interference fringe pattern on a detector. Using numerical simulations, we show that the SAM can estimate rapidly varying tip-tilt errors in space telescopes arising from line-of-sight pointing oscillations as well as other higher-order modes. We also show that a Kalman filter can be used with the SAM to improve the estimation. At Princetons High Contrast Imaging Laboratory, we have recently created a testbed devoted to low-order wavefront sensing experiments. The testbed incorporates custom-fabricated masks (shaped pupil, focal plane, and sparse aperture) with a deformable mirror and a CCD camera to demonstrate the estimation and correction of low-order aberrations. Our first experiments aim to replicate the results of the SAM wavefront sensor (SAM WFS) Fourier propagation models.