This paper investigates the characteristics of higher-order transverse mode fully clamped membrane resonators that are piezoelectrically transduced as a class of resonators that completely seal the domain above the resonator from the domain below. Such isolation between the top and bottom of a resonator is preferable when encasing the device in a microfluidic cell for liquid-phase sensing measurements, a setup that can be beneficial for sensing applications. Most fully clamped membrane resonators are hampered by low liquid-phase quality factor (Q) and large motional resistance (R
m). This paper describes the design of higher-order transverse (2, 2) mode square membrane and (2, 0) mode circular membrane resonators, and the effect of device scaling on liquid-phase Q and R
m. We show a best-case liquid-phase R
m of 54 kΩ and Q of 270 among the various membrane sizes tested. This level of liquid-phase Q is higher than some contour mode resonators. Compared to other fully clamped membrane resonators in the literature, the results here represent a significant improvement in both R
m and Q, highlighting the potential of these membrane resonators for liquid-phase mass sensing applications.