The transmission potential of a novel infection depends on both the inherent transmissibility of a pathogen, and the level of susceptibility in the host population. However, distinguishing between these pathogen- and population-specific properties typically requires detailed serological studies, which are rarely available in the early stages of an outbreak. Using a simple transmission model that incorporates age-stratified social mixing patterns, we present a novel method for characterizing the transmission potential of subcritical infections, which have effective reproduction number R<1, from readily available data on the size of outbreaks. We show that the model can identify the extent to which outbreaks are driven by inherent pathogen transmissibility and pre-existing population immunity, and can generate unbiased estimates of the effective reproduction number. Applying the method to real-life infections, we obtained accurate estimates for the degree of age-specific immunity against monkeypox, influenza A(H5N1) and A(H7N9), and refined existing estimates of the reproduction number. Our results also suggest minimal pre-existing immunity to MERS-CoV in humans. The approach we describe can therefore provide crucial information about novel infections before serological surveys and other detailed analyses are available. The methods would also be applicable to data stratified by factors such as profession or location, which would make it possible to measure the transmission potential of emerging infections in a wide range of settings.