A variant of pulsed-field-ionisation zero-kinetic-energy photoelectron spectroscopy (PFI-ZEKE-PES) has been developed to determine the position of ionic energy levels with an accuracy limited by the bandwidth of the tunable photoexcitation source. The development relies on the ability of resolving the transitions to the high Rydberg states (n similar or equal to 200) which contribute to each line in a PFI-ZEKE photoelectron spectrum using a near-Fourier-transform-limited extreme ultraviolet (XUV) laser system (bandwidth <250 MHz). Thwe lowest ionisation potentials of Ar and N-2 have been determined from Rydberg-state-resolved PFI-ZEKE-PE spectra to be (127109.8250.015) cm(-1) and (125667.028 +/-0.015) cm(-1), respectively.