TaRh2B2 and NbRh2B2 compounds exhibit noncentrosymmetric superconductivity with a chiral structure. Density functional theory-based ab-initio calculations have been executed to analyze the structural properties, mechanical stability, ductility/brittleness behaviors, Debye temperature, melting temperature, optical response to incident photon energy, electronic characteristics, and superconducting transition temperature of chiral TaRh2B2 and NbRh2B2 compounds under pressure up to 16 GPa. Both the chiral phases are mechanically stable and exhibit ductile nature under the studied pressure. The maximum value of the Pugh ratio (an indicator of ductile/brittle behaviors) is observed to be 2.55 (for NbRh2B2) and 2.52 (for TaRh2B2) at 16 GPa. The lowest value of the Pugh ratio is noticed at 0 GPa for both these chiral compounds. The analysis of reflectivity spectra suggests that both the chiral compounds can be used as efficient reflecting materials in the visible energy region. At 0 GPa, the calculated densities of states (DOSs) at the Fermi level are found to be 1.59 and 2.13 states eV-1 per formula unit for TaRh2B2 and NbRh2B2, respectively. The DOS values of both the chiral phases do not alter significantly with applied pressure. The shape of the DOS curve of both compounds remains almost invariant with applied pressure. The pressure-induced variation of Debye temperatures of both compounds is observed, which may cause the alternation of the superconducting transition temperature, Tc, with applied pressure. The probable changing of Tc with pressure has been analyzed from the McMillan equation.