A central issue in randomness generation is to estimate the entropy of the output data generated by a given device. Here we present a protocol for self-testing quantum random number generation, in which the entropy of the raw data can be monitored in real-time. In turn, this allows the user to adapt the randomness extraction procedure, in order to continuously generate high quality random bits. Using a fully optical implementation, we demonstrate that our protocol is practical and efficient, and illustrate its self-testing capacity.