We propose to measure the importance of spin-orbit couplings (SOCs) in the nonadiabatic molecular quantum dynamics rigorously with quantum fidelity. To make the criterion practical, quantum fidelity is estimated efficiently with the multiple-surface dephasing representation (MSDR). The MSDR is a semiclassical method that includes nuclear quantum effects through interference of mixed quantumclassical trajectories without the need for the Hessian of potential energy surfaces. Two variants of the MSDR are studied, in which the nuclei are propagated either with the fewest-switches surface hopping or with the locally mean field dynamics. The fidelity criterion and MSDR are first tested on one-dimensional model systems amenable to numerically exact quantum dynamics. Then, the MSDR is combined with “on-the-fly” computed electronic structure to measure the importance of SOCs and nonadiabatic couplings in the photoisomerization dynamics of CH2NH 2 considering 20 electronic states and in the collision of F + H2 considering six electronic states.