Borate complexes that contain tridentate ligands tris(o-oxyaryl)methanes and -silanes were synthesized. These complexes had a cage-shaped structure around a boron center. The geometry of the structure determined the properties of the borates in which ligands were consistently bound to the metal center by chelation. Theoretical calculations suggested that the cage-shaped borates had a large dihedral angle (C_ipso-O-B-O) compared with open-shaped borates. The large angle leads to a greater Lewis acidity for cage-shaped borates. Substitution of a bridgehead Si for a bridgehead C decreased the Lewis acidity due to its smaller dihedral angle. The introduction of electron-withdrawing groups on the aryl moieties in the cage-shaped framework increased the Lewis acidity. The cage-shaped borates effectively catalyzed some organic transformations more than the open-shaped borate B(OPh)₃. Selective recognition of aromatic aldehyde over aliphatic aldehyde was accomplished in a catalytic manner by using cage-shaped borates with a π-pocket.