The source Swift J1644+5734 is the first-known transient that has extremely luminous non-thermal emission from radio to γ-ray wavelengths (Bloom et al. Galaxies: individual: Swift J1644+5734, galaxies: jets, radio continuum: galaxies 1 INTRODUCTION This tight limit is direct observational evidence for either a very small viewing angle or a strong jet deceleration due to interactions with a dense circum-nuclear medium, in agreement with some recent theoretical studies. We conclude that the apparent average ejection speed between 2012.2 was less than 0.3 c with a confidence level of 99 per cent. No proper motion has been detected in the Swift J1644+5734 radio ejecta. This is one of the best phase-referencing measurements available to date. With respect to the in-beam source FIRST J1644+5736, we have achieved a statistical astrometric precision about 12 μas (68 per cent confidence level) per epoch. Our observing strategy was to identify a very nearby and compact radio source with the real-time e-EVN, and then utilize this source as a stationary astrometry reference point in the later five deep EVN observations. In order to directly measure the apparent speed of the radio jet, we performed very long baseline interferometry (VLBI) observations with the European VLBI network (EVN) at 5 GHz. The first-known tidal disruption event (TDE) with strong evidence for a relativistic jet – based on extensive multiwavelength campaigns – is Swift J1644+5734.