The parallel and perpendicular components of the static dipole polarizabilities of the title molecules in different spectroscopic states were calculated using a large variety of high-level electron correlation methods. Excitation energies between different states for C-2 are presented as well. We used both single-reference coupled-cluster methods at different level of sophistication and complete active space SCF, multireference configuration interaction, and averaged quadratic coupled-cluster methods with various active spaces. The reliability of calculated properties for BeO and C-2, known as difficult to calculate accurately, was deduced from the pattern of results observed by a systematic improvement of the level of sophistication and from a comparison of coupled-cluster and multireference variational methods.