Stellar evolutionary models simulate binary stars well, when the individual stellar mass and the system metallicity are known. Our main goal in this paper is to determine a set of stellar parameters (mass, age, helium abundance and convection parameters) for binary systems formed by FGK main-sequence stars of Population I. For a selected group of seven binaries, where luminosity, effective temperature, gravity and metallicity are experimentally observed, we estimate the above-mentioned set of stellar parameters (and provide estimation errors) by fitting simulated quantities to those observed. For each system, we estimate all such parameters and their respective estimation errors, including individual masses (despite the fact that these are known for these stars with an accuracy of 3 per cent). The observational mass is recovered by the models with an absolute error of 0.02 M⊙ (on average). Half of the stars considered have a mixing-length parameter not compatible to the solar value, possibly because of the mild observed rotation of these stars. However, the error bars show that all these systems can be modelled using a solar helium-to-metal chemical enrichment parameter. Except for NGC 188 KR V12, our results fit into what has been obtained or predicted in previous works. Finally, we find a tendency for a decrease of the mixing-length parameter and an increase of the overshooting with an increase of the mass. The analysis of these seven binaries and the corresponding 14 stars shows that stellar solar models are not able to reproduce the observations in most of the cases, mainly because of the subsolar mixing-length parameter. We suspect that the non-solar values obtained might be a result of the absence of rotation in the models.