The existence of a nonzero permanent electric dipole moment (EDM) of the neutron would reveal a new source of CP violation and shed light on the origin of the matter-antimatter asymmetry of the Universe. The sensitivity of current experiments using stored ultracold neutrons (UCN) probes new physics beyond the TeV scale. Using the UCN source at the Paul Scherrer Institut, the nEDM collaboration has performed the most sensitive measurement of the neutron EDM to date, still compatible with zero (|d_n|<1.8×10^-26ecm, C.L.90%). A new experiment designed to improve the sensitivity by an order of magnitude, n2EDM, is currently in construction.