We systematically explore the stability and properties of [B12X11Ng]− adducts resulting from the capture reaction of noble gas atoms (Ng) by anionic [B12X11]− clusters in the ion trap. [B12X11]− can be obtained by stripping one X− ligand off the icosahedral closo-dodecaborate dianion [B12X12]2−. We study the binding of the noble gas atoms He, Ne, Kr, Ar and Xe to [B12X11]− with ligands X = F, Cl, Br, I, CN. While He cannot be captured by these clusters and Ne only binds at low temperatures, the complexes with the heavier Kr, Ar and Xe show appreciable complexation energies and exceed 1 eV at room temperature in the case of [B12(CN)11Xe]−. For the latter three noble gases, we observe a significant charge transfer from the Ng to the icosahedral B12 cage.