We report a comprehensive design procedure for passively Q-switched monolithic Nd:YAG/Cr4+:YAG microchip lasers to realize operation conditions of the pulse repetition rate (PRR) >100kHz and pulse width (PW) <400ps, simultaneously. Crucial parameters including effective pump power and waist diameter of the pump laser, doping concentration and thickness of the Nd:YAG crystal, initial transmittance (T0) of the Cr4+:YAG crystal, as well as the reflectivity of the output coupler are all considered during the design process. Two single-longitudinal-mode-operated lasers are designed and constructed according to the numerical results. The lengths and doping concentrations of Nd:YAG for both microchips are optimized to be 0.5 mm and 2%, respectively. A PRR up to 170 kHz and PW of ∼370ps are measured under the pump power of 2.6 W for a microchip with T0 of 0.85. A slightly lower PRR of 118 kHz with a shorter PW of ∼320ps is also achieved under the same pump power for another microchip with T0 of 0.8. The related pulse energies for the two microchips are ∼2.1µJ and ∼1.8µJ, respectively. To the best of our knowledge, these results are among the highest PRRs achieved for passively Q-switched Nd:YAG/Cr4+:YAG microchips with PWs <400ps.