The Kepler mission and subsequent ground-based follow-up observations have revealed a number of exoplanet host stars with nearby stellar companions. This study presents speckle observations of 57 Kepler objects of interest (KOIs) that are also double stars, each observed over a 3-8yr period, which has allowed us to track their relative motions with high precision. Measuring the position angle and separation of the companion with respect to the primary can help determine if the pair exhibits common proper motion, indicating it is likely to be a bound binary system. We report on the motions of 34 KOIs that have close stellar companions, three of which are triple stars, for a total of 37 companions studied. Eighteen of the 34 systems are confirmed exoplanet hosts, including one triple star, while four other systems have been subsequently judged to be false positives and twelve are yet to be confirmed as planet hosts. We find that 21 are most likely to be common proper motion pairs, 4 are line-of-sight companions, and 12 are of an uncertain disposition at present. The fraction of the confirmed exoplanet host systems that are common proper motion pairs is approximately 86% in this sample. In this subsample, the planets are exclusively found with periods of less than 110 days, so that in all cases the stellar companion is found at a much larger separation from the planet host star than the planet itself. A preliminary period-radius relation for the confirmed planets in our sample suggests no obvious differences at this stage with the full sample of known exoplanets.