For a dielectric sphere, Mie scattering gives:
Can be used to compute the interaction between two spheres:
"Casimir Forces between Arbitrary Compact Objects,"
T. Emig, N. Graham, R.L. Jaffe, & M. Kardar, Phys. Rev. Lett. 99, 170403 (2007)
Between a sphere and a plane:
"Fluctuation induced quantum interactions between compact objects and a plane mirror,"
T. Emig, J. Stat. Mech. P04007 (2008)
Can be generalized to finite temperatures and imperfect conductivity
"Quantum and thermal Casimir interaction between a sphere and a plate: Comparison of Drude and plasma models,"
R. Zandi, T. Emig, & U. Mohideen, Phys. Rev. B 81, 195423 (2010)