The nearest millisecond pulsar PSR J0437–4715 is the ideal target to constrain the dense matter equation of state using the lightcurve modelling method. Our analysis combining XMM-Newton, NuSTAR, and ROSAT observations removed ambiguities in the spectral modelling of the surface emission from PSR J0437–4715. Furthermore, the NuSTAR observation demonstrated that the non-thermal hard tail emission was pulsed at the pulsar spin period. These features are crucial to model the lightcurve and to measure the radius of the neutron star. This conference proceeding is based on the publication Guillot et al. (2016).