We study the performance exhibited by transport protocols, TCP and QUIC, over realistic satellite networks. We propose a novel methodology, which combines real implementation (exploiting virtualization techniques) and simulation, to carry out systematic and repetitive experiments. We modify the default operation of the ns-3 framework and we integrate the dynamism that characterizes links in satellite communications, particularly links to LEO satellites. We carry out a thorough assessment over different setups, changing the operating band and the buffer length. In addition, we ascertain the impact of using the multi-streaming feature that QUIC includes. The results show that QUIC yields lower delays than TCP, although in particular setups it might suffer from higher jitter. In addition, using multiple streams in QUIC does not yield a relevant gain. In any case, we can conclude that the behavior of transport protocols over non-terrestrial-networks might not be always optimum and that QUIC can bring benefits when compared to TCP.