For the multivariate calibration problem assuming a multivariate linear regression model, an asymptotic confidence region for the parameter of interest is derived. The confidence region is shown to always include the maximum likelihood estimate for the parameter of interest. The exact confidence region for the parameter of interest was derived by Mathew and Kasala (1994). This exact region includes not only the maximum likelihood estimate for the parameter of interest, but other estimates which do not maximize the likelihood function. It is shown that the exact region can result in many separate or overlapping regions, only one of which contains the maximum likelihood estimate. Asymptotic confidence regions and exact confidence regions were calculated for two examples of real multivariate data sets.