Studying transient phenomena with the Very Long Baseline Interferometry (VLBI) technique faces severe difficulties because the turnaround time of the experiments from the observations to the scientific result is rather long. The e-VLBI technique has made it possible to transfer the data from a number of European VLBI Network (EVN) telescopes to the central data processor at JIVE through optical fibres, and correlate them in real time. The main goal of this paper is to introduce this rapidly developing new technique, by presenting observational results from a recent experiment. We observed SN2001em, a Type Ib/c supernova with an e-VLBI array and the Multi-Element Radio Linked Interferometer Network (MERLIN) in the UK. The source is marginally detected in our observations. We cannot make definite conclusions whether it is resolved at 1.6 GHz or not. Our data show that SN2001em either started fading in the last couple of months, or its radio spectrum is inverted at low frequencies,indicating free-free or synchrotron self-absorption. This is quite unusual, but not unprecedented in radio SNe.