question: Studies aimed at characterizing the evolution of COVID-19 disease often rely on case-based surveillance data publicly released by health authorities, that can be incomplete and prone to errors. Here, we quantify the biases caused by the use of inaccurate data in the estimation of the Time-Varying Reproduction Number R(t). By focusing on Italy and Spain, two of the hardest-hit countries in Europe and worldwide, we show that if the symptoms' onset time-series is inferred from the notification date series, the R(t) curve cannot capture nor describe accurately the early dynamics of the epidemic. Furthermore, the effectiveness of the containment measures that were implemented, such as national lockdowns, can be properly evaluated only when R(t) is estimated using the real time-series of dates of symptoms' onset. Our findings show that extreme care should be taken when a pivotal quantity like R(t) is used to make decisions and to evaluate different alternatives.