Addendum: some very intense, point-blank EMP-ish effects can bother 'Mechs, including an arriving HPG pulse, the EMP mine of TR2750, and (previously) magnetic pulse warheads used to be able to wobble a fusion reactor's magnetic field, though software changes have largely negated MPWs.
Generally, though, 'Mechs and other modern BT warmachines are not greatly bothered by EMP.