We evaluated the effect of a radio frequency shield on the signal-to-noise ratio (SNR) of a loop coil at various field strengths in simulation. At 7T, SNR constantly improves as the shield diameter increases. At higher field strengths, SNR is maximized when using an optimal shield diameter, which is inversely proportional to the frequency. We also show that central SNR for a 32-channel receive array could drop by a factor of two when using a non-optimal shield diameter at 10.5T. Inserting a transmit array between the receiver and an optimally-sized shield could considerably deteriorate SNR.