Recognition memory is thought to consist of two component processes--recollection and familiarity. It has been suggested that the hippocampus supports recollection, while adjacent cortex supports familiarity. However, the qualitative experiences of recollection and familiarity are typically confounded with a quantitative difference in memory strength (recollection > familiarity). Thus, the question remains whether the hippocampus might in fact support familiarity-based memories whenever they are as strong as recollection-based memories. We addressed this problem in a novel way by using the Remember/Know procedure, which allowed us to explicitly match the confidence and accuracy of Remember and Know decisions. As in earlier studies, recollected items had higher accuracy and confidence than familiar items, and hippocampal activity was higher for recollected items than for familiar items. Furthermore, hippocampal activity was similar for familiar items, misses, and correct rejections. When the accuracy and confidence of recollected and familiar items were matched, the findings were dramatically different. Hippocampal activity was now similar for recollected and familiar items. Importantly, hippocampal activity was also greater for familiar items than for misses or correct rejections (as well as for recollected items vs misses or correct rejections). Our findings suggest that the hippocampus supports both recollection and familiarity when memories are strong.