  The Medium Resolution Spectrometer on board JWST/MIRI will give access to
mid-IR spectra while retaining spatial information. With the unparalleled
sensitivity of JWST and the MIRI detectors, the MRS has the potential to
revolutionise our understanding of giant exoplanet atmospheres. Molecular
mapping is a promising detection and characterisation technique used to study
the spectra of directly imaged exoplanets. We aim to examine the feasibility
and application of this technique to MRS observations. We used the instrument
simulator MIRISIM to create mock observations of resolved star and exoplanet
systems. As an input for the simulator, we used stellar and planet parameters
from literature, with the planet spectrum being modelled with the radiative
transfer code petitRADTRANS. After processing the raw data with the JWST
pipeline, we high pass filter the data to account for the stellar point spread
function, and used a forward modelling approach to detect the companions and
constrain the chemical composition of their atmospheres through their molecular
signatures. We identified limiting factors in spectroscopic characterisation of
directly imaged exoplanets with the MRS and simulated observations of two
representative systems, HR8799 and GJ504. In both systems, we could detect the
presence of multiple molecules that were present in the input model of their
atmospheres. We used two different approaches with single molecule forward
models, used in literature, that are sensitive to detecting mainly H$_2$O, CO,
CH$_4$, and NH$_3$, and a log-likelihood ratio test that uses full atmosphere
forward models and is sensitive to a larger number of less dominant molecular
species. We show that the MIRI MRS can be used to characterise widely separated
giant exoplanets in the mid-IR using molecular mapping.
