The magnetic properties of the antiferromagnet CeNiSnH and of the ferromagnet CeNiSnH(1.8) on hydrostatic pressure (0≤P≤10.8 bar) have been determined using a miniature piston-cylinder CuBe pressure cell. With increasing P, the Néel temperature of CeNiSnH increases weakly from 4.77 to 5.01 K whereas the Curie temperature of CeNiSnH(1.8) decreases rapidly from 7.16 to 5.30 K. Similar pressure dependence is also observed in the critical field of the metamagnetic transition of CeNiSnH and in the coercive field of CeNiSnH(1.8). Electronic structure calculations for these hydrides within the density functional theory show agreement with the experimental findings. Detailed examination of the chemical bonding features point to the conclusion that the antibonding Ce-Ni states below the Fermi level for CeNiSnH(1.8) could be responsible for the decrease of its Curie temperature under applied pressure.