In the current literature, there are few experimental tests of capacities for cumulative cultural evolution in nonhuman species. There are even fewer examples of such tests in young children. This limited evidence is noteworthy given widespread interest in the apparent distinctiveness of human cumulative culture, and the potentially significant theoretical implications of identifying related capacities in nonhumans or very young children. We evaluate experimental methods upon which claims of capacities for cumulative culture, or lack thereof, have been based. Although some of the established methods (those simulating generational succession) have the potential to identify positive evidence that fulfills widely accepted definitions of cumulative culture, the implementation of these methods entails significant logistical challenges. This is particularly true for testing populations that are difficult to access in large numbers, or those not amenable to experimental control. This presents problems for generating evidence that would be sufficient to support claims of capacities for cumulative culture, and these problems are magnified for establishing convincing negative evidence. We discuss alternative approaches to assessing capacities for cumulative culture, which circumvent logistical problems associated with experimental designs involving chains of learners. By inferring the outcome of repeated transmission from the input–output response patterns of individual subjects, sample size requirements can be massively reduced. Such methods could facilitate comparisons between populations, for example, different species, or children of a range of ages. We also detail limitations and challenges of this alternative approach, and discuss potential avenues for future research.