Based on a provided closed-form wireless power transmission (WPT) efficiency formula, which may be used for any value of load, we have analyzed the WPT efficiencies between two metamaterial-inspired loop antennas in various aspects. Due to the modeling based on low frequency circuit theory, the provided formula at the center resonant frequency has been found to be accurate until when the distance between the two loop antennas increases to 15 cm (about $lambda_0/6$ at 300 MHz). When the two loops get closer, the resonant frequency has been found to split into two in theory, simulations, and measurements. The EM-simulated and measured efficiencies at new resonant frequencies are 60.9 % and 46.3 %, respectively, at d=15 cm. With two extra rings around the loops, the maximum efficiency is enhanced to 93.7 % at d=15 cm. The effect of the additional two rings is about 30 %.