A calorimetric technique and a calculation procedure to obtain excess enthalpies H-E of liquid mixtures is described and tested. It is based on a heat-how calorimeter used as a titration calorimeter to measure the heat effects associated to small additions of one of the components, or a mixture of them, to the ampoule containing a known amount of the other component or of a mixture of them. The procedure takes into account the presence of a small vapour space and calculates the heat involved in the vapour-liquid equilibration after each addition. The experimental values are fitted with a parametric equation such as Redlich-Kister to determine the H-E parameters by least-squares adjustment. The technique has been tested with respect to the systems ethanol + cyclohexane, dioxane + water and tetrachloromethane + benzene. The results show a good agreement with literature data for these mixtures, and confirm the capability of this technique to reliably replace the mix-flow technique when the components mix slowly, or show a mixture gap, or are available in small quantities. H-E results are reported for the system perfluorohexane + hexane for which the mixing process is slow.