Narrow-line Seyfert 1 galaxies (NLS1) are active galactic nuclei (AGN) known to have small masses of the central black hole and high accretion rates. NLS1s are generally radio-quiet, but a small part of them (about 7%) are radio-loud. The recent discovery of powerful relativistic jets in radio-loud NLS1s (RLNLS1s), emitting at high-energy $γ$-rays, opened intriguing questions. The observed luminosity of the jet is generally weak, smaller than blazars, although when rescaled for the mass of the central black hole, it becomes of the same order of magnitude of the latter. The weak luminosity, and hence observed flux, resulted in a small number of known RLNLS1. From a recent survey of RLNLS1s, it was found that only 8 out of 42 sources had radio flux density at 1.4 GHz greater than 100 mJy, while 21 out of 42 had flux density smaller than 10 mJy. In addition, given the strong variability at all wavelengths, with present-day facilities RLNLS1s can often only be detected during high activity periods. The Square Kilometer Array (SKA), with its superior sensitivity, will break this limit, allowing us to unveil a relatively unknown population of jetted AGN. We present the results of a study aimed at evaluating the scenario that could emerge after the advent of SKA.