Abstract The continuum-fitting and the iron-line methods are currently the two leading techniques for measuring the spins of accreting black holes. In the past few years, these two methods have been developed for testing fundamental physics. In the present work, we employ state-of-the-art models to test black holes through the continuum-fitting and the iron-line methods and we analyze three NuSTAR observations of the black hole binary GRS 1716-249 during its outburst in 2016–2017. In these three observations, the source was in a hard-intermediate state and the spectra show both a strong thermal component and prominent relativistic reflection features. Our analysis confirms the Kerr nature of the black hole in GRS 1716-249 and provides quite stringent constraints on possible deviations from the predictions of general relativity.