Constrained multiobjective optimisation problems (CMOPs) are common in real-world optimisation. They often involve expensive solution evaluations and, therefore, it is helpful to know the best methods to solve them prior to actually solving them. These problems also tend to be relatively difficult for algorithms compared to the majority of test problems. This difficulty often presents itself in the infeasible region, calling for a focus on the constraint handling technique (CHT). The purpose of this work is to select the best CHT for problems with difficult constraint functions. This first involves the collection of a set of such problems. CHT selection is then conducted using problem characterisation and machine learning. The outcomes are positive in that prediction achieved a high accuracy. Additionally, further insights are provided into the features that describe CMOPs.