We report on the systematic characterization of Ba(Fe$_{0.92}$Co$_{0.08}$)$_2$As$_2$ epitaxial thin films on CaF$_2$ substrate in view of their possible use for superconducting electronic applications. By using different and complementary techniques we studied the morphological characteristics of the surface, the structural properties, the magnetic response, and the superconducting properties in terms of critical temperature, critical current, and energy gaps. Particular attention was paid to the homogeneity of the films and to the comparison of their superconducting properties with those of single crystals of the same compound.