  Gyrochronology can yield useful ages for field main-sequence stars, a regime
where other techniques are problematic. Typically, gyrochronology relations are
calibrated using young ($\lesssim 2$ Gyr) clusters, but the constraints at
older ages are scarce, making them potentially inaccurate and imprecise. In
order to test the performance of existing relations, we construct samples of
stellar pairs with coeval components, for a range of ages and with available
rotation periods. These include randomly paired stars in clusters, and wide
binaries in the Kepler field. We design indicators that, based on the measured
rotation periods and expectations from gyrochronology, quantify the
(dis)agreement between the coeval pairs and the gyrochronology calibrations
under scrutiny. Our results show that wide binaries and cluster members are in
better concordance with gyrochronology than samples of randomly paired field
stars, confirming that the relations have predicting power. However, the
agreement with the examined relations decreases for older stars, revealing a
degradation of the examined relations with age, in agreement with recent works.
This highlights the need for novel empirical constraints at older ages that may
allow revised calibrations. Notably, using coeval stars to test gyrochronology
poses the advantage of circumventing the need for age determinations while
simultaneously exploiting larger samples at older ages. Our test is independent
of any specific age-rotation relation, and it can be used to evaluate future
spin-down models. In addition, taking gyrochronology at face value, we note
that our results provide new empirical evidence that the components of field
wide binaries are indeed coeval.
