People with persistently asymptomatic severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection experience no symptoms throughout the course of infection, while pre-symptomatic individuals report symptoms attributable to the virus. Transmission of SARS-CoV-2 from individuals without symptoms contributes to pandemic spread, but the extent of transmission from persistently asymptomatic individuals remains unknown. We describe three methodological issues that hinder attempts to estimate this proportion. First, incomplete symptom assessment likely overestimates the asymptomatic fraction. Second, studies with inadequate follow-up misclassify pre-symptomatic individuals. Third, serological studies may identify people with previously unrecognized infection, but reliance on poorly defined antibody responses and retrospective symptom assessment may result in misclassification. We provide recommendations regarding definitions, detection, documentation and follow-up to improve the identification and evaluation of people with persistently asymptomatic SARS-CoV-2 infection and their contacts. Accurate characterisation of the persistently asymptomatic fraction may shed light on COVID-19 pathogenesis, transmission dynamics, and inform public health responses.