  On large ground-based telescopes, the combination of extreme adaptive optics
(ExAO) and coronagraphy with high-dispersion spectroscopy (HDS), sometimes
referred to as high-dispersion coronagraphy (HDC), is starting to emerge as a
powerful technique for the direct characterisation of giant exoplanets. The
high spectral resolution not only brings a major gain in terms of accessible
spectral features but also enables a better separation of the stellar and
planetary signals. Ongoing projects such as Keck/KPIC, Subaru/REACH, and
VLT/HiRISE base their observing strategy on the use of a few science fibres,
one of which is dedicated to sampling the planet's signal, while the others
sample the residual starlight in the speckle field. The main challenge in this
approach is to blindly centre the planet's point spread function (PSF)
accurately on the science fibre, with an accuracy of less than 0.1 $\lambda/D$
to maximise the coupling efficiency. In the context of the HiRISE project,
three possible centring strategies are foreseen, either based on
retro-injecting calibration fibres to localise the position of the science
fibre or based on a dedicated centring fibre. We implemented these three
approaches, and we compared their centring accuracy using an upgraded setup of
the MITHiC high-contrast imaging testbed, which is similar to the setup that
will be adopted in HiRISE. Our results demonstrate that reaching a
specification accuracy of 0.1 $\lambda/D$ is extremely challenging regardless
of the chosen centring strategy. It requires a high level of accuracy at every
step of the centring procedure, which can be reached with very stable
instruments. We studied the contributors to the centring error in the case of
MITHiC and we propose a quantification for some of the most impacting terms.
