  In the era of large-scale surveys of stars in the Milky Way, stellar ages are
crucial for studying the evolution of the Galaxy. But determining ages of field
stars is notoriously difficult; therefore, we attempt to determine benchmark
ages for the extensively studied Gaia benchmark stars which can be used for
validation purposes. By searching the literature for age estimates from
different methods and deriving new ages based on Bayesian isochrone fitting, we
are able to put reliable limits on the ages of 16 out of the 33 benchmark
stars. The giants with well-defined ages are all young, and an expansion of the
sample to include older giants with asteroseismic ages would be beneficial.
Some of the stars have surface parameters inconsistent with isochrones younger
than 16 Gyr. Including $\alpha$-enhancement in the models when relevant
resolves some of these cases, but others clearly highlight discrepancies
between the models and observations. We test the impact of atomic diffusion on
the age estimates by fitting to the actual surface metallicity of the models
instead of the initial value and find that the effect is negligible except for
a single turn-off star. Finally, we show that our ability to determine
isochrone-based ages for large spectroscopic surveys largely mirrors our
ability to determine ages for these benchmark stars, except for stars with
$\log g \gtrsim 4.4$ dex since their location in the HR diagram is almost age
insensitive. Hence, isochrone fitting does not constrain their ages given the
typical uncertainties of spectroscopic stellar parameters.
