Conformational free-energy differences are key quantities for understanding important phenomena in molecular biology that involve large structural changes of macromolecules. In this paper, an improved version of the confinement approach, which is based on earlier developments, is used to determine the free energy of individual molecular states by progressively restraining the corresponding molecular structures to pure harmonic basins, whose absolute free energy can be computed by normal-mode analysis. The method is used to calculate the free-energy difference between two conformational states of the alanine dipeptide in vacuo, and of the beta-hairpin from protein G with an implicit solvation model. In all cases, the confinement results are in excellent agreement with the ones obtained from converged equilibrium molecular dynamics simulations, which have a much larger computational cost. The systematic and statistical errors of the results are evaluated and the origin of the errors is identified. The sensitivity of the calculated free-energy differences to structure-based definitions of the molecular states is discussed. A variant of the method, which closes the thermodynamic cycle by a quasi-harmonic rather than harmonic analysis, is introduced. The latter is proposed for possible use with explicit solvent simulations.