Our understanding of the magnetic fields of stars is nearly monopolized by knowledge of our own sun. Very-long baseline radio interferometry (VLBI) provides a means of directly imaging the radio coronae of other stars at a high enough resolution to discern discrete features, something not possible with other observational methods. It also allows the highest positional accuracy of any observational method available. This thesis details the VLBI study of two nearby radio-loud stars in close binary systems. Both systems were observed at numerous epochs spaced over a range of several months with the global-scale radio interferometer array the VLBA-HSA. These observations were combined with archival data from the National Radioastronomy Observatory (NRAO) Archive. The resulting positions, as well as previously published positions, were used to calculate a least-squares solution for all the orbital and astrometric parameters of both systems. This made it possible to determine the position of the physical star with respect to the radio emission in each image. The images of both stars were found to conform to theoretical emission produced by a model dipolar magnetosphere with a filled or partially-filled coronal loop.