Various models have been developed to simulate rainfall interception by vegetation but their formulations and applications rely on a number of assumptions and parameter estimation procedures. The aim of this study is to examine the effect of different model assumptions and parameter derivation approaches on the performance of the Rutter, Gash and Liu interception models. The Rutter model, in contrast to the other two daily models, was applied both on an hourly and on a daily basis. Hourly data from a meteorological station, one automatic and 28 manual throughfall gauges from a semi-arid Pinus brutia forest (Cyprus) for the period between 01/Jul/2016 and 31/May/2020 were used for the analysis. We conducted a sensitivity analysis for the assessment of the model parameters and variables: canopy storage capacity (S), canopy cover fraction (c), the ratio of mean wet evaporation rate to mean wet rainfall rate (Ēc/R̄) and potential evaporation (Eo). Three parameter derivation approaches were tested: the widely used regression method and an automatic model parameterization procedure for optimization of S and c and for optimization of S (with c observed). The parameterized models were run with daily meteorological data and compared with long-term weekly throughfall data (2008–2019). The Gash and Liu models showed low sensitivity to Ēc/R̄. Test runs with different combinations of S, c and Ēc/R̄ revealed strong equifinality. The models showed high performance for both calibration and validation periods with Kling–Gupta Efficiency (KGE) above 0.90. Gash and Liu models with the automatic model parameterization procedures resulted in higher KGEs than with the regression method. The interception losses computed from the long-term application of the three models ranged between 18 and 20%. The models were all capable of capturing the inherently variable interception process. However, a representative time series of throughfall measurements is needed to parameterize the models.