Recently, the unusual behaviour of the specific heat of the superconductors YBa₂Cu₃O₇, Y₂Ba₄Cu₇O₁₅, and YBa₂Cu₄O₈ at high field and low temperature was attributed to Zeeman splitting of localized states in the vortex cores. In an attempt to detect similar effects in classic high-κ superconductors, we have measured the mixed-state specific heat of NbSe₂ single crystals in magnetic fields up to Hc2(0). The specific heat in the superconducting state and zero field is found to follow accurately a strong-coupling model that takes into account the anisotropy of the gap. We analyse then the mixed-state specific heat using the London model. A small Schottky-like excess specific heat remains unexplained. In qualitative agreement with the observations made in Y-Ba-Cu-O, this contribution is suggested to originate from the localized vortex core levels observed by STM techniques.