Mathematical models of the coronary circulation have been shown to provide useful information for the analysis of intracoronary blood flow and pressure measurements acquired during coronary artery bypass graft (CABG) surgery. Although some efforts towards the patient-specific estimation of model parameters have been presented in this context, they are based on simplifying hypotheses about the collateral circulation and do not take advantage of the whole set of data acquired during CABG. In order to overcome these limitations, this paper presents an exhaustive parameter sensitivity analysis and a multiobjective patient-specific parameter estimation method, applied to a model of the coronary circulation of patients with triple vessel disease. The results of the sensitivity analysis highlighted the importance of capillary and collateral development. On the other hand, the estimation method was applied to intraoperative clinical data from ten patients obtained during CABG, which permitted to assess patient-specific collateral vessel situations. These approaches provide new insights regarding the heterogeneous configuration of the collateral circulation.