Several methods have been proposed for overcoming the effects of radiofrequency (RF) magnetic field inhomogeneity in high-field MRI. Some of these methods rely at least in part on the ability to independently control magnitude and phase of different drives in either one multielement RF coil or in different RF coils in a transmit array. The adjustment of these drive magnitudes and phases alone to create uniform RF magnetic (B(1)) fields has been called RF shimming, and has certain limits at every frequency as dictated by possible solutions to Maxwell's equations. Here we use numerical calculations to explore the limits of RF shimming in the human head. We found that a 16-element array can effectively shim a single slice at frequencies up to 600 MHz and the whole brain at up to 300 MHz, while an 80-element array can shim the whole brain at up to 600 MHz.