We present a method to estimate myocardial blood flow confidence intervals (MBF-CI) for model-based analysis of CT myocardial perfusion imaging (CT-MPI). We have determined that good fits, as assessed with visual evaluation, root-mean-square error, and Akaike information criterion (AIC), can lead to very poor MBF estimates with >50% error. We develop the use of confidence intervals to help confirm that good models are leading to good MBF estimates. We assess MBF precision for multiple analysis models from the literature, including adiabatic approximation of tissue homogeneity (AATH), plasma tissue uptake (PTU), and a newly proposed robust physiologic model (RPM). For evaluation, we use a physiologic simulator, digital CT-MPI phantom, and in vivo CT-MPI data from a porcine model of coronary stenosis. MBF-CI was calculated using empirical likelihood to determine the range of MBF values that fall within the 95% joint parameter confidence region. On simulated data, although AIC was smallest (preferred) for AATH and greatest for RPM, standard deviation of MBF measurements was between 7-41 times greater for AATH than RPM, indicating RPM significantly improved MBF precision. MBF-CI appropriately selected RPM for best MBF precision. For the SNR=20 example condition, standard deviations were 1.7, 28.4, and 34.7mL/min/100g; MBF-CIs were 26, 375, and 435mL/min/100g; and AICs were 299.7, 253.4, and 245.3 for RPM, PTU, and AATH, respectively. Overall, best MBF precision was ranked RPM>PTU>AATH. These findings suggest that models with fewer free parameters, such as RPM, yield precise MBF measurements and that MBF-CI can select for models with good MBF measurement precision.