Phenomena that occur only at high pressures in bulk phases are often observed in nanopores, suggesting that the pressure in such confined phases is large. We report a molecular simulation study of the pressure tensor of an argon nanophase within slit-shaped carbon pores and show that the tangential pressure is positive and large, while the normal pressure can be positive or negative depending on pore width. We also show that small changes in the bulk pressure have a large effect on the tangential pressure, suggesting that it should be possible to control the latter over wide ranges in laboratory experiments.