We propose a new methodology aimed at finding star-forming galaxies in the phase which immediately follows the star-formation ( SF ) quenching , based on the use of high- to low-ionization emission line ratios . These ratios rapidly disappear after the SF halt , due to the softening of the UV ionizing radiation . We focus on [ O III ] \lambda 5007/H \alpha and [ Ne III ] \lambda 3869/ [ O II ] \lambda 3727 , studying them with simulations obtained with the CLOUDY photoionization code . \textcolor black If a sharp quenching is assumed , we find that the two ratios are very sensitive tracers as they drop by a factor \sim 10 within \sim 10 Myr from the interruption of the SF ; instead , if a smoother and slower SF decline is assumed ( i.e . an exponentially declining star-formation history with e -folding time \tau = 200 Myr ) , they decrease by a factor \sim 2 within \sim 80 Myr . We mitigate the ionization – metallicity degeneracy affecting our methodology using pairs of emission line ratios separately related to metallicity and ionization , adopting the [ N II ] \lambda 6584/ [ O II ] \lambda 3727 ratio as metallicity diagnostic . Using a Sloan Digital Sky Survey galaxy sample , \textcolor blackwe identify 10 examples among the most extreme quenching candidates within the [ O III ] \lambda 5007/H \alpha vs. [ N II ] \lambda 6584/ [ O II ] \lambda 3727 plane , characterized by low [ O III ] \lambda 5007/H \alpha , \textcolor blackfaint [ Ne III ] \lambda 3869 , and by blue dust-corrected spectra and ( u - r ) colours , as expected if the SF quenching has occurred in the very recent past . Our results also suggest that the observed fractions of quenching candidates can be used to constrain the quenching mechanism at work \textcolor blackand its time-scales .