Computational cost often hinders the calibration of complex computer models. In this context, history matching (HM) is becoming a widespread calibration strategy, with applications in many disciplines. HM uses a statistical approximation, also known as an emulator, to the model output, in order to mitigate computational cost. The process starts with an observation of a physical system. It then produces progressively more accurate emulators to determine a non-implausible domain: a subset of the input space that provides a good agreement between the model output and the data, conditional on the model structure, the sources of uncertainty, and an implausibility measure. In HM, it is essential to generate samples from the nonimplausible domain, in order to run the model and train the emulator until a stopping condition is met. However, this sampling can be very challenging, since the nonimplausible domain can become orders of magnitude smaller than the original input space very quickly. This paper proposes a solution to this problem using subset simulation, a rare event sampling technique that works efficiently in high dimensions. The proposed approach is demonstrated via calibration and robust design examples from the field of aerospace engineering.