We describe a scheme for finding quantum critical points based on studies of a nonequilibrium susceptibility during finite-rate quenches taking the system from one phase to another. We assume that two such quenches are performed in opposite directions and argue that they lead to the formation of peaks of a nonequilibrium susceptibility on opposite sides of a critical point. Its position is then narrowed to the interval marked off by these values of the parameter driving the transition, at which the peaks are observed. Universal scaling with the quench time of precision of such an estimation is derived and verified in two exactly solvable models. The experimental relevance of these results is expected.