Earth will become uninhabitable within 2-3 Gyr as a result of the increasing luminosity of the Sun changing the boundaries of the habitable zone (HZ). Predictions about the future of habitable conditions on Earth include declining species diversity and habitat extent, ocean loss, and changes to geochemical cycles. Testing these predictions is difficult, but the discovery of a planet that is an analogue to future Earth could provide the means to test them. This planet would need to have an Earth-like biosphere history and to be approaching the inner edge of the HZ at present. Here, we assess the possibility of finding such a planet and discuss the benefits of analyzing older Earths. Finding an old-Earth analogue in nearby star systems would be ideal, because this would allow for atmospheric characterization. Hence, as an illustrative example, G stars within 10 pc of the Sun are assessed as potential old-Earth-analog hosts. Six of these represent good potential hosts. For each system, a hypothetical Earth analogue is placed at locations within the continuously habitable zone (CHZ) that would allow enough time for Earth-like biosphere development. Surface temperature evolution over the host star's main sequence lifetime (assessed by using a simple climate model) is used to determine whether the planet would be in the right stage of its late-habitable lifetime to exhibit detectable biosignatures. The best candidate, in terms of the chances of planet formation in the CHZ and of biosignature detection, is 61 Virginis. However, planet formation studies suggest that only a small fraction (0.36%) of G stars in the solar neighborhood could host an old-Earth analogue. If the development of Earth-like biospheres is rare, requiring a sequence of low-probability events to occur, biosphere evolution models suggest they are rarer still, with only thousands being present in the Galaxy as a whole.