We present a numerical method to compute defect-free textures inside cholesteric domains of arbitrary shape. This method has two interesting properties, namely a robust and fast quadratic convergence to a local minimum of the Frank free energy, thanks to a trust region strategy. We apply this algorithm to study the texture of cholesteric droplets in coexistence with their isotropic liquid in two cases: when the anchoring is planar and when it is tilted. In the first case, we show how to determine the anchoring energy at the cholesteric-isotropic interface from a study of the optical properties of droplets of different sizes oriented with an electric field. This method is applied to the case of the liquid crystal CCN-37. In the second case, we come back to the issue of the textural transition as a function of the droplet radius between the double-twist droplets and the banded droplets, observed for instance in cyanobiphenyl liquid crystals. We show that, even if this transition is dominated by the saddle-splay Gauss constant K4, as was recently recognized by Yoshioka et al. [Soft Matter 12, 2400 (2016)], the anchoring energy does also play an important role that cannot be neglected.