Computer models, whilst frequently utilised for many complex engineering tasks, suffer from model form errors due to some level of simplification and/or absence of certain physics. These model form errors lead to a mismatch between model outputs and observational data when the ‘true’ parameters are known; a phenomenon known as model discrepancy. Calibration of a computer model without consideration of this type of uncertainty therefore leads to biased estimates of system parameters. Bayesian history matching (BHM) is one such method of calibrating a computer model whilst accounting for uncertainties associated with model discrepancy. The ‘likelihood-free’ technique assesses the system parameter domain using an emulator of the complex computer model in order to discard parameter combinations based on how unlikely they were to have produced a known observation response. BHM can be approached in an iterative manner, allowing sequential-based approaches to be used in selecting new computer model evaluations that will maximise the improvement in emulator performance. This paper develops techniques for sequentially selecting new computer model evaluations, reducing the total number of evaluations and increasing improvements in the emulator. The developed metrics and criteria are outlined with a demonstration on a numerical case study in order to visually demonstrate their applicability and increase in computational efficiency.