We theoretically and numerically investigated procedures for accurately determining the acoustical physical constants of piezoelectric hexagonal (class 6mm) crystals, taking ZnO as an example, using bulk-wave velocities and leaky surface acoustic wave (LSAW) velocities acquired by ultrasonic microspectroscopy technology. Selection of appropriate propagation modes and directions for eight velocity measurements to facilitate accurately determining five elastic constants (c11E, c12E, c13E, c33E, and c44E) and three piezoelectric constants (e15, e31, and e33) was discussed in addition to measurements of two dielectric constants (ε11S and ε33S) and the density (ρ). Several determination procedures were obtained. Using only bulk-wave velocities measured for Y-cut, Z-cut, and several rotated Y-cut crystalline plane specimens provided the best determination accuracies for constants c13E, c33E, e31, and e33. Favorable determination accuracies were also achieved using several sets of two rotated Y-cut crystalline plane specimens such as (101) and (102). Conductive specimens of (001) and (102) with a resistive (103) specimen made the bulk-wave measurements simpler, resulting in greatly improved determination accuracies. The additional use of LSAW velocity with one conductive (001) specimen enabled the determination procedures to be simplified, resulting - in acceptable accuracy for c13E. Measurements of bulk-wave velocities and LSAW velocities for just two resistive Y-cut and Z-cut specimens could determine all the constants, albeit with some deterioration in accuracy, especially for e31 and e33. This will be useful for preliminary determination of the constants for precious crystals.