Power transfer efficiency (PTE) and power delivered to the load (PDL) are key inductive link design parameters for powering millimeter-sized implants. While several groups have suggested increasing the power carrier frequency (fp) of inductive links to 100s of MHz to maximize PTE, we have demonstrated that operating at 10s of MHz offers higher allowable PDL under the safety absorption rate (SAR) constraints. We have proposed a closed-form power function that relates maximum power levels that can safely be transferred at different frequencies under the SAR constraints. Three sets of inductive links at different frequencies of 50 MHz, 200 MHz, and 400 MHz have been optimized for powering a 1 mm(3)-sized implant. We have shown in simulations that reducing fp from 200 MHz to 50 MHz along with shrinking the size of the transmitter coil results in ~7.8 times higher PDL under SAR constraints, at the cost of only 52% drop in PTE.