A Monte Carlo Bloch solver has been developed and used to establish the bias and uncertainty of T1, T2 values in primary reference solutions for MRI phantoms. Errors and uncertainties are on the order of 1% when using a NMR system and robust pulse sequences. Errors and uncertainties in MRI systems are much larger, 5% to 40% for T1 values. The Monte Carlo Bloch solver can help determine uncertainties and imperfections in a scanner and then determine the bias and uncertainty of measured biomarkers for different pulse sequences. At present, the source of the large errors and scanner-to-scanner variation in T1 and T2 measured using the NIST/ISMRM system phantom are unknown.