Young massive stars are usually found embedded in dense massive molecular clumps and are known for being highly obscured and distant. During their formation process, deuteration is regarded as a potentially good indicator of the very early formation stages. In this work, we test the observability of the ground-state transition of ortho-H$_2$D$^+$ $J_{rm {K_a, K_c}} = 1_{10}$-$1_{11} $ by performing interferometric and single-dish synthetic observations using magneto-hydrodynamic simulations of high-mass collapsing molecular cores, including deuteration chemistry. We studied different evolutionary times and source distances (from 1 to 7 kpc) to estimate the information loss when comparing the column densities inferred from the synthetic observations to the column densities in the model. We mimicked single-dish observations considering an APEX-like beam and interferometric observations using CASA and assuming the most compact configuration for the ALMA antennas. We found that, for centrally concentrated density distributions, the column densities are underestimated by about 51% in the case of high-resolution ALMA observations ($leqslant$1) and up to 90% for APEX observations (17). Interferometers retrieve values closer to the real ones, however, their finite spatial sampling results in the loss of contribution from large-scale structures due to the lack of short baselines. We conclude that, the emission of o-H$_2$D$^+$ in distant massive dense cores is faint and would require from $sim$1 to $sim$7 hours of observation at distances of 1 and 7 kpc, respectively, to achieve a 14$sigma$ detection in the best case scenario. Additionally, the column densities derived from such observations will certainly be affected by beam dilution in the case of single-dishes and spatial filtering in the case of interferometers.
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