One of the key design considerations for biomedical implants is to minimize the system volume while achieving high performance. An attractive approach to power biomedical implants is to use wireless power transfer (WPT) with ultrasound. To receive the ultrasonic energy, a piezoelectric transducer is implemented, which is designed to have the resonance frequency at the frequency of the ultrasonic wave. To extract the received energy from the transducer, an energy rectification circuit is typically required. The commonly used rectifier is called a synchronized switch harvesting on inductor (SSHI) rectifier, which employs an inductor to increase the energy efficiency. However, the employment of inductor limits the system miniaturization since it usually needs to be around 1's mH. The synchronized switch harvesting on capacitors (SSHC) rectifier was recently proposed to be used on vibration energy harvesting and this architecture achieves inductor-less fully integrated design. In a vibration energy harvesting system, the piezoelectric transducer usually has large inherent capacitance and low resonant frequency. But the piezoelectric transducer used in ultrasonic WPT typically has very small capacitance and much higher resonant frequency. In this paper, the performance of a SSHC rectifier used in ultrasonic WPT is analyzed. The analysis covers system size and performance. Based on the analysis, this paper presents an important design consideration on designing a SSHC rectifier to be used in ultrasonic WPT, which is the allowed maximal ON resistance in the capacitor-to-capacitor charging loop in function of the transducer capacitance, transducer resonant frequency and the number of SSHC stages.