The angular, magnetic field, and temperature dependence of the Eu2+ (4 f7, S=7/2) g -value in Ca1-x Eux B6 (0.15 x≤1.00) is measured by means of electron spin resonance at two microwave frequencies, 9.4 and 34.4 GHz. The g -value is found to be anisotropic and magnetic-field-dependent. The reduction with field of the positive g -shift is interpreted in terms of the exchange interaction between the localized Eu2+ 4 f7 electrons with the conduction Eu2+ 5d -like electrons and B 2p -like holes. The angular, temperature, and x dependence of the anisotropy of the g -value can be attributed to demagnetization effects due to the platelet-like shape of the samples. High-resolution synchrotron x-ray diffraction experiments show the absence of distortions larger than δa/a∼ 10-4. However, a mechanism for the anisotropy based on a weak tetragonal lattice distortion arising from the crystal surface cannot be excluded. © 2006 The American Physical Society.