We report new magnetic field measurements for 14 classical T Tauri stars (CTTSs). We combine these data with one previous field determination in order to compare our observed field strengths with the field strengths predicted by magnetospheric accretion models. We use literature data on the stellar mass, radius, rotation period, and disk accretion rate to predict the field strength that should be present on each of our stars according to these magnetospheric accretion models. We show that our measured field values do not correlate with the field strengths predicted by simple magnetospheric accretion theory. We also use our field strength measurements and literature X-ray luminosity data to test a recent relationship expressing X-ray luminosity as a function of surface magnetic flux derived from various solar feature and main-sequence star measurements. We find that the T Tauri stars we have observed have weaker than expected X-ray emission by over an order of magnitude on average using this relationship. We suggest the cause for this is actually a result of the very strong fields on these stars, which decreases the efficiency with which gas motions in the photosphere can tangle magnetic flux tubes in the corona.