Cardiac mitochondria are intracellular organelles that participate significantly in the intracellular calcium cycle. A dysfunction in calcium signaling by mitochondria could thus affect the excitation-contraction coupling of myocytes. We proposed previously a mathematical model for calcium signaling by cardiac mitochondria, in order to better understand their underlying role. With 34 parameters, our model is simple in comparison with models in the literature, yet it is still impossible to fit experimental data. For this reason, and to quantify the effects of uncertainties on the parameters of the model, we performed a global sensitivity analysis using Sobol indices. Firstly, we highlighted the parameters with little influence on fluxes governing the activity of the mitochondria, whi\ ch are internal components of our model. Secondly, with these parameters fixed in their range of uncertainty, we repeated the analysis on the solution of the ordinary differential equations, taking into consideration only the influential parameters from the first step. The latter analysis showed that only six parameters have an important influence on the respiratory rates of the mitochondria. Finally, using a genetic optimization algorithm, we calibrated these six parameters, using two different experimental datasets, which describe oxygen concentration variation in time. The same resulting set of parameter fits well the two datasets, with up to 3.2% relative l2 error. Hence, the model was able to reproduce correct respiratory rates in both state 3 (phosphorylating), and substrate-state of mitochondria. Subsequently, we expect repeated sensitivity analysis with additional experimental data, reflecting calcium but also reactive oxygen species, to allow for more parameters to be calibrated.