We present results of high-resolution spectroscopic observations of detached eclipsing binaries (DEBs) with total eclipses, for which UVES spectra were obtained during the phase of totality. These observations serve as a key way to determine the age and initial metallicity of the systems and to verify evolutionary phases of their components and distances. With the additional, independent information concerning the effective temperature and metallicity of one of the components, we aim to estimate the precise ages of the studied binaries and show the usefulness of totality spectra. The second goal was to provide precise orbital and physical stellar parameters of the components of systems in question. Using the VLT/UVES, we obtained high-resolution spectra of 11 DEBs during their total-eclipse phase. Atmospheric parameters of then-visible (larger) components were obtained with With additional spectroscopy from the Comprehensive Research with \'Echelles on the Most interesting Eclipsing binaries ( project, public archives, and literature, we obtained radial-velocity (RV) measurements, from which orbital parameters were calculated. Photometric time-series observations from TESS and ASAS were modelled with the JKTEBOP code, and, combined with RV-based results, they allowed us to obtain physical parameters for nine double-lined systems from our sample. All the available data were used to constrain the ages with our own approach, utilising MESA isochrones. Reddening-free, isochrone-based distances were also estimated and confronted with Gaia Data Release 3 (GDR3) results. We show that single spectroscopic observations taken during a total eclipse can break the age-metallicity degeneracy and allow for the precise determination of the age of a DEB. With high-quality spectroscopic and photometric data, we are able to reach a 5-10<!PCT!> level of uncertainty (e.g. $724^ $ Myr). Even for single-lined DEBs, where absolute masses are not possible to obtain, the spectroscopic analysis of one of the components allows one to put strong constraints on the properties of both stars. For some cases, we noted inconsistencies between isochrone-based and GDR3 distances. For one binary, which could not be fitted with a single isochrone (RZ Eri), we suggest a new explanation.