Knowing where our limbs are in space is essential for moving and for adapting movements to various changes in our environments and bodies. The ability to adapt movements declines with age, and age-related cognitive decline can explain a decreased ability to adopt and deploy explicit, cognitive strategies in motor learning. Age-related sensory decline could also lead to a reduced fidelity of sensory position signals and error signals, each of which can affect implicit motor adaptation. Here we investigate two estimates of limb position; one based on proprioception, the other on predicted sensory consequences of movements. Each is considered a measure of an implicit adaptation process and may be affected by both age and cognitive strategies. Both older (n = 38) and younger (n = 42) adults adapted to a 30° visuomotor rotation in a centre-out reaching task. We make an explicit, cognitive strategy available to half of participants in each age group with a detailed instruction. After training, we first quantify the explicit learning elicited by instruction. Instructed older adults initially use the provided strategy slightly less than younger adults but show a similar ability to evoke it after training. This indicates that cognitive explanations for age-related decline in motor learning are limited. In contrast, training induced much larger shifts of state estimates of hand location in older adults compared to younger adults. This is not modulated by strategy instructions, and appears driven by recalibrated proprioception, which is almost twice as large in older adults, while predictions might not be updated in older adults. This means that in healthy aging, some implicit processes may be compensating for other changes to maintain motor capabilities, while others also show age-related decline (data: https://osf.io/qzhmy).