SARS-CoV-2 vaccines give rise to positive externalities on population health, society and the economy in addition to protecting the health of vaccinated individuals. Hence, the social value of such a vaccine exceeds its market value. This paper estimates the willingness to pay (WTP) for a hypothetical SARS-CoV-2 vaccine in four countries, namely the United States (US), the United Kingdom (UK), Spain and Italy during the first wave of the COVID-19 pandemic when no specific vaccine had been approved nor subsidised. WTP estimates are elicited using a payment card method to avoid 'yea saying' biases, and we study the effect of protest responses, sample selection bias, as well as the influence of trust in government and risk exposure when estimating the WTP. Our estimates suggest evidence of an average value of a hypothetical vaccine of 100-200 US dollars once adjusted by purchasing power parity (PPP). Estimates are robust to a number of checks.