Pinch points for heat exchanger network synthesis were determined using rigorously calculated thermodynamic properties, in contrast with the usual approach of assuming constant heat capacities (c(P)) and linear interpolations in enthalpy for phase changing streams. We discuss a more formal approach to the energy targeting problem, showing that its solution requires the use of a global minimization method, because of the possibility of multiple local minima in the objective function. We show three applications, two of them involving near-critical streams and the other containing several streams that undergo phase transitions. In all cases, we correctly detected pinch points that otherwise would have been wrongly located by targeting procedures based on the constant c(P) assumption and on a single linearization between the bubble and dew points for each stream. For this reason, the procedure presented here is an adequate alternative for the accurate determination of pinch points and utility targets when the physical properties have nonlinear behavior with respect to temperature.