An in silico study is performed to assess the noble gas (Ng) binding ability of 1-tris(pyrazolyl)borate beryllium and magnesium cationic complexes (TpBe⁺ and TpMg⁺). The Be and Mg centers in these complexes are found to bind heavier Ng atoms quite effectively. Both the zero point energy and basis set superposition error corrected dissociation energy values for the bonds between Ar–Rn and metal atoms range within 5.8–10.2 kcal mol⁻¹ for Be and within 5.2–9.9 kcal mol⁻¹ for Mg. The dissociation of the Kr–Rn bound analogues of TpBe⁺ and Ar–Rn bound analogues of TpMg⁺ into the individual Ng atoms and TpBe⁺ or TpMg⁺ complexes is endergonic in nature at room temperature. The remaining lighter Ng bound complexes would be stable at lower temperatures. The nature of Be–Ng or Mg–Ng bonds is explored via Wiberg bond indices computation, atoms-in-molecules and energy decomposition analyses. The degree of covalent character in the Be/Mg–Ng bonds increases gradually in moving from He to its heavier congeners. The Be–Xe/Rn and Mg–Xe/Rn bonds could be categorized as being of the partial covalent type. The contribution from the orbital term is at the maximum towards the total attraction. The magnitude of this term becomes gradually larger from He to Rn, implying a larger degree of covalent character for heavier Ng atoms.