Before highly automated vehicles (HAVs) become part of everyday traffic, their safety has to be proven. The use of human performance as a benchmark represents a promising approach, but appropriate methods to quantify and compare human and HAV performance are rare. By adapting the method of constant stimuli, a scenario-based approach to quantify the limit of (human) performance is developed. The method is applied to a driving simulator study, in which participants are repeatedly confronted with a cut-in manoeuvre on a highway. By systematically manipulating the criticality of the manoeuvre in terms of time to collision, humans’ collision avoidance performance is measured. The limit of human performance is then identified by means of logistic regression. The calculated regression curve and its inflection point can be used for direct comparison of human and HAV performance. Accordingly, the presented approach represents one means by which HAVs’ safety performance could be proven.