The global minimum geometries of BeCN2 and BeNBO are linear BeN-CN and BeN-BO, respectively. The Be center of BeCN2 binds He with the highest Be-He dissociation energy among the studied neutral He-Be complexes. In addition, BeCN2 can be further tuned as a better noble gas trapper by attaching it with any electron-withdrawing group. Taking BeO, BeS, BeNH, BeNBO, and BeCN2 systems, the study at the CCSD(T)/def2-TZVP level of theory also shows that both BeCN2 and BeNBO systems have higher noble gas binding ability than those related reported systems. ΔG values for the formation of NgBeCN2/NgBeNBO (Ng = Ar-Rn) are negative at room temperature (298 K), whereas the same becomes negative at low temperature for Ng = He and Ne. The polarization plus the charge transfer is the dominating term in the interaction energy.