The origin of the high X-ray luminosities of most ultraluminous X-ray sources (ULXs) still remains poorly understood. Most of the scenarios proposed to explain their nature assume that ULXs are powered by accretion on to a black hole (BH). In this case, the detection of compact radio emission and the location of the ULXs in the Fundamental Plane (X-ray versus radio-luminosity plane) can provide an estimate of the ULX BH mass and help address the question of their physical nature. We present the results of a high-resolution (very long baseline interferometry) radio observational campaign aimed at detecting and studying compact radio emission in four ULXs with known radio counterparts. We find that one of the targets (N4559-X4) was previously misclassified: its low X-ray luminosity indicates that the source is not a ULX. No milliarcsec-scale radio emission is detected for N4559-X4 nor for the ULXs N4490-X1 and N5194-X2, for which upper limits on the radio luminosities are estimated. These limits argue strongly against the presence of supermassive BHs in these three systems. For N4559-X4, the low X-ray luminosity and the ratio of the radio and X-ray luminosities suggest the presence of an X-ray binary. Compact radio emission is detected for the ULX N5457-X9 within its Chandra positional error, making N5457-X9 a potential intermediate-mass BH with steady jet emission.