Aims: We have identified several tens of extremely metal-poor star candidates from SDSS and LAMOST, which we follow up with the 4.2 m William Herschel Telescope (WHT) telescope to confirm their metallicity. Methods: We followed a robust two-step methodology. We first analyzed the SDSS and LAMOST spectra. A first set of stellar parameters was derived from these spectra with the FERRE code, taking advantage of the continuum shape to determine the atmospheric parameters, in particular, the effective temperature. Second, we selected interesting targets for follow-up observations, some of them with very low-quality SDSS or LAMOST data. We then obtained and analyzed higher-quality medium-resolution spectra obtained with the Intermediate dispersion Spectrograph and Imaging System (ISIS) on the WHT to arrive at a second more reliable set of atmospheric parameters. This allowed us to derive the metallicity with accuracy, and we confirm the extremely metal-poor nature in most cases. In this second step we also employed FERRE, but we took a running mean to normalize both the observed and the synthetic spectra, and therefore the final parameters do not rely on having an accurate flux calibration or continuum placement. We have analyzed with the same tools and following the same procedure six well-known metal-poor stars, five of them at [Fe/H] <-4 to verify our results. This showed that our methodology is able to derive accurate metallicity determinations down to [Fe/H] <-5.0. Results: The results for these six reference stars give us confidence on the metallicity scale for the rest of the sample. In addition, we present 12 new extremely metal-poor candidates: 2 stars at [Fe/H] ≃-4, 6 more in the range -4 < [Fe / H] < -3.5, and 4 more at -3.5 < [Fe / H] < -3.0. Conclusions: We conclude that we can reliably determine metallicities for extremely metal-poor stars with a precision of 0.2 dex from medium-resolution spectroscopy with our improved methodology. This provides a highly effective way of verifying candidates from lower quality data. Our model spectra and the details of the fitting algorithm are made public to facilitate the standardization of the analysis of spectra from the same or similar instruments. The model spectra are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/605/A40