Recent unambiguous experiments (melting of ultrafine particles, premelting at the surface of a bulk crystal, superheating, etc.) offer clear evidence of the key role of the surface in determining the melting of a material. In this work we concentrate our attention on spherical and non-spherical nanometric lead inclusions. We report experimental results on Pb/SiO and Pb/Al2O3 systems obtained at different temperatures by two techniques: high-sensitivity optical reflectance and dark-field electron microscopy. The main result is the existence, below the melting temperature and at the surface of the inclusion, of a liquid layer whose thickness is much larger than that observed on the bulk (zero curvature). This thickness, which depends on local curvature, increases continuously with temperature until a uniform curvature of the solid core is attained; then the core melts suddenly. A phenomenological model, based on the minimization of the free energy, is proposed and reported in detail. It represents a significant improvement compared to previous theoretical approaches related to well-known thermodynamic size-effect models, particularly insofar as the agreement with the experimental results is concerned.