We report on the nonlinear optical response of CdSe nanoplatelets and CdSe/CdS core/shell nanoplatelets in the heavy-hole resonant excitonic transition spectral regions with femtosecond pulses. The nonlinear refraction and saturable absorption coefficients were obtained using the Z-scan technique, and the results were explained theoretically. The nonlinear optical response under nonresonant excitation has been previously examined; comparing with the results presented in this work, at least a one order of magnitude increase in the nonlinear refraction coefficient is evident.