Boron complexes that contain new tridentate ligands, tris(o-oxyaryl)methanes and -silanes, were prepared. These complexes had a cage-shaped structure around a boron center and showed higher Lewis acidity and catalytic activity than open-shaped boron compounds. The cage-shaped ligands determined the properties of the borates by altering the geometry and were consistently bound to the metal center by chelation. The synthesized compounds were L⋅B(OC(6)H(4))(3)CH, L⋅B(OC(6)H(4))(3)SiMe, and its derivatives (L=THF or pyridine as an external ligand). Theoretical calculations suggested that the cage-shaped borates had a large dihedral angle (C(ipso)-O-B-O) compared with open-shaped borates. The geometric effect due to the dihedral angle means that compared with open-shaped, the cage-shaped borates have a greater Lewis acidity. The introduction of electron-withdrawing groups on the aryl moieties in the cage-shaped framework increased the Lewis acidity. Substitution of a bridgehead Si for a bridgehead C decreased the Lewis acidity of the boron complexes because the large silicon atom reduces the dihedral angle of C(ipso)-O-B-O. The ligand-exchange rates of the para-fluoro-substituted compound B(OC(6)H(3)F)(3)CH and the ortho-phenyl-substituted compound B(OC(6)H(3)Ph)(3)CH were less than that of the unsubstituted borate B(OC(6)H(4))(3)CH. The ligand-exchange rate of B(OC(6)H(4))(3)SiMe was much faster than that of B(OC(6)H(4))(3)CH. A hetero Diels-Alder reaction and Mukaiyama-type aldol reactions were more effectively catalyzed by cage-shaped borates than by the open-shaped borate B(OPh)(3) or by the strong Lewis acid BF(3) ⋅OEt(2). The cage-shaped borates with the bulky substituents at the ortho-positions selectively catalyzed the reaction with less sterically hindered substrates, while the unsubstituted borate showed no selectivity.