In order to achieve efficient wireless power transmission (WPT) to biomedical implants with millimeter (mm) dimensions, ultrasonic WPT links have recently been proposed. Operating both transmitter (Tx) and receiver (Rx) ultrasonic transducers at their resonance frequency (fr) is key in improving power transmission efficiency (PTE). In this paper, different resonance configurations for Tx and Rx transducers, including series and parallel resonance, have been studied to help the designers of ultrasonic WPT links to choose the optimal resonance configuration for Tx and Rx that maximizes PTE. The geometries for disk-shaped transducers of four different sets of links, operating at series-series, series-parallel, parallel-series, and parallel-parallel resonance configurations in Tx and Rx, have been found through finite-element method (FEM) simulation tools for operation at f_r of 1.4 MHz. Our simulation results suggest that operating the Tx transducer with parallel resonance increases PTE, while the resonance configuration of the mm-sized Rx transducer highly depends on the load resistance, Rl. For applications that involve large Rl in the order of tens of kΩ, a parallel resonance for a mm-sized Rx leads to higher PTE, while series resonance is preferred for Rl in the order of several kΩ and below.