Power transmission efficiency (PTE) has been the key parameter for wireless power transmission (WPT) to biomedical implants with millimeter (mm) dimensions. It has been suggested that for mm-sized implants increasing the power carrier frequency (f) of the WPT link to hundreds of MHz improves PTE. However, increasing f significantly reduces the maximum allowable power that can be transmitted under the specific absorption rate (SAR) constraints. This paper presents a new figure-of-merit (FoM) and a design methodology for optimal WPT to mm-sized implants via inductive coupling by striking a balance between PTE and maximum delivered power under SAR constraints (P). First, the optimal mm-sized receiver (Rx) coil geometry is identified for a wide range of f to maximize the Rx coil quality factor (Q). Secondly, the optimal transmitter (Tx) coil geometry and f are found to maximize the proposed FoM under a low-loss Rx matched-load condition. Finally, proper Tx coil and tissue spacing is identified based on FoM at the optimal f. We demonstrate that f in order of tens of MHz still offer higher P and FoM, which is key in applications that demand high power such as optogenetics. An inductive link to power a 1 mm implant was designed based on our FoM and verified through full-wave electromagnetic field simulations and measurements using de-embedding method. In our measurements, an Rx coil with 1 mm diameter, located 10 mm inside the tissue, achieved PTE and P of 1.4% and 2.2 mW at f of 20 MHz, respectively.