  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
\textit{Chandra} positional error, making N5457-X9 a potential
intermediate-mass BH with steady jet emission.
