Binary systems, in particular eclipsing binaries, are essential sources of knowledge of the fundamental properties of stars. The ages of binaries, members of open clusters, are constrained by their own fundamental properties and by those of the hosting cluster. The ages of eleven open clusters are here found by constructing models for the components of twelve eclipsing binaries. The difference between the ages we find and the ages of the clusters derived from isochrone fitting is up to 40%. For the binary system V497 Cep in NGC 7160, the difference is about 100%. Binary systems whose primary component is about to complete its main-sequence lifetime, such as V453 Cyg and V906 Sco, are the most suitable systems for age determination. Using model results for these stars, we derive an expression for sensitive and uncomplicated relative age determination of binary systems (age divided by the main-sequence lifetime of the primary star). The expression is given as a logarithm of radii ratio divided by a logarithm of mass ratio. Two advantages of this expression are that: (i) it is nearly independent of the assumed chemical composition of the models because of the appearance of the ratio of radii; and (ii) the ratios of radii and masses are observationally much more precise than their absolute values. We also derive another expression using luminosities rather than radii and compare results.