The mooring system of floating wave energy converters (WECs) has a crucial impact on power generation efficiency, cost of delivered energy, proper operation, reliability and survivability. An effective design, addressing such competing objectives, requires appropriate mathematical models to predict mooring loads and dynamic response. However, conversely to traditional offshore engineering applications, experience in modelling mooring systems for WECs is limited, due to their unique requirement of maximising the motion while minimising loads and costs. Even though modelling approaches and software are available for this application, guidelines and critical comparison are still scarce. This paper proposes a discussion and validation of three mooring-line models: one quasi-static approach (developed in-house) and two dynamic lumped-mass approaches (the open source MoorDyn and the commercial OrcaFlex). The case study is a 1:32-scale prototype of a floating oscillating water column WEC tested in a wave tank, with three mooring lines, each one comprising of a riser and a clump weight. Validation, performed by imposing fairlead displacements and comparing resulting tensions, shows good agreement. The small scale may induce numerical instabilities and uncertainties in the parameter estimation. Finally, likely due to internal resonance of this particular mooring system, high-frequency content in the mooring tension is found, albeit absent in the kinematics of the floater.