Consensus clustering (CC) has been adopted for unsupervised class discovery in many genomic studies. It calculates how frequently two samples are grouped together in repeated clustering runs, and uses the resulting pairwise "consensus rates" for visual demonstration that clusters exist, for comparing cluster stability, and for estimating the optimal cluster number (K). However, the sensitivity and specificity of CC have not been systemically assessed. Through simulations we find that CC is able to divide randomly generated unimodal data into apparently stable clusters for a range of K, essentially reporting chance partitions of cluster-less data. For data with known structure, the common implementations of CC perform poorly in identifying the true K. These results suggest that CC should be applied and interpreted with caution. We found that a new metric based on CC, the proportion of ambiguously clustered pairs (PAC), infers K equally or more reliably than similar methods in simulated data with known K. Our overall approach involves the use of realistic null distributions based on the observed gene-gene correlation structure in a given study, and the implementation of PAC to more accurately estimate K. We discuss the strength of our approach in the context of other ensemble-based methods.