Broad band pulsar radiation can be effectively used to monitor the properties of the magneto-ionic media through which it propagates. Faraday rotation calculated from polarised pulsar observations provides an integrated product of electron densities and the line-of-sight component of the magnetic field in the intervening plasma. In particular, a time-variable effect mainly associated with the rapidly changing column density of the Earth’s ionosphere and plasmasphere heavily dominates the observed Faraday rotation of pulsar radiation. In this work, we aim to carry out a performance test of three GNSS-based models of the ionosphere using observations of PSR J0332+5434 taken with the LOw Frequency ARray (LOFAR). As it was shown in Porayko et al. (Month Not Roy Astron Soc 483(3):4100–4113, 2019. https://doi.org/10.1093/mnras/sty3324. arXiv:1812.01463), the conventional single layer model (SLM), which assumes that the ionosphere is a thin slab at a fixed effective height, is not capable of fully accounting for the ionospheric Faraday rotation in pulsar data. The simplified physics of the SLM is upgraded within IRI-Plas (International Reference Ionosphere and Plasmasphere) extended SLM and the dual-layer voxel TOmographic Model of the Ionosphere (TOMION), both of which partially account for the thickness and vertical dynamics of the terrestrial plasma. Although the last two improve the reconstruction of the ionospheric Faraday rotation, none of the considered models completely purge the observed residual variations. With this study, we show that the long term LOFAR observations of Faraday rotation of pulsars provide an excellent tool to test and improve models of the magneto-ionic content of the Earth’s atmosphere.