When it comes to modelling complex systems using an agent-based approach, there is a problem of choosing the appropriate parameter optimisation technique. This problem is further aggravated by the fact that the parameter space in complex agent-based systems can have a large dimension, and the time required to perform numerical experiments can be large. An alternative approach to traditional optimisation methods are the so-called metaheuristic algorithms, which provide an approximate solution in an acceptable time. The purpose of this study is to compare various metaheuristic algorithms for parameter tuning and to analyse their effectiveness applied to two agent-based models with different complexities. In this study, we considered commonly used metaheuristic algorithms for agent-based model optimisation: the Markov chain Monte Carlo method, the surrogate modelling approach, the particle swarm optimisation algorithm, and the genetic algorithm, as well as the more novel chaos game optimisation algorithm. The proposed algorithms were tested on two agent-based models, one of which was a simple toy model of the spread of contagious disease, and the other was a more complex model of the circulation of respiratory viruses in a city with 10 million agents and 26 calibrated parameters.