© ESO, 2015. Context. With the current study we aim at understanding the properties of radio emission and the assumed jet from four radio-loud and γ-ray-loud narrow-line Seyfert 1 galaxies that have been detected by Fermi. These are Seyfert 1 galaxies with emission lines at the low end of the FWHM distribution. Aims. The ultimate goal is twofold: first we investigate whether a relativistic jet is operating at the source producing the radio output, and second, we quantify the jet characteristics to understand possible similarities with and differences from the jets found in typical blazars. Methods. We relied on the most systematic monitoring of radio-loud and γ-ray-detected narrow-line Seyfert 1 galaxies in the cm and mm radio bands conducted with the Effelsberg 100 m and IRAM 30 m telescopes. It covers the longest time-baselines and the most radio frequencies to date. This dataset of multi-wavelength, long-term radio light-curves was analysed from several perspectives. We developed a novel algorithm to extra