This paper presents a new approach using artificial neural networks (ANN) to determine the thermodynamic properties of two alternative refrigerant/absorbent couples (LiCl–H₂O and LiBr + LiNO₃ + LiI + LiCl–H₂O). These pairs can be used in absorption heat pump systems, and their main advantage is that they do not cause ozone depletion. In order to train the network, limited experimental measurements were used as training and test data. Two feedforward ANNs were trained, one for each pair, using the Levenberg–Marquardt algorithm. The training and validation were performed with good accuracy. The correlation coefficient obtained when unknown data were applied to the networks was 0.9997 and 0.9987 for the two pairs, respectively, which is very satisfactory. The present methodology proved to be much better than linear multiple regression analysis. Using the weights obtained from the trained network, a new formulation is presented for determination of the vapor pressures of the two refrigerant/absorbent couples. The use of this new formulation, which can be employed with any programming language or spreadsheet program for estimation of the vapor pressures of fluid couples, as described in this paper, may make the use of dedicated ANN software unnecessary.