How does one measure biological age without knowing chronological age? Biomarkers: quantitative measurements of endpoints that have been shown to be correlated with natural aging.

Tom Johnson has a recent review (ScienceDirect | DOI) on the subject, well worth checking out for a solid introduction to the current state of the art and the challenges ahead:

This communication reviews recent papers attempting to identify Biomarkers of Aging (BoA). A BoA is a biological parameter that will predict functional capability at some later age. Few, if any, BoA have been found and this review describes the recent search for BoA. Among others that have been put forward are IL6 and other markers of inflammation, allostatic load, and corticosterone, which have been described primarily in humans. Work in model systems as well as theoretical work are also reviewed.