Let $\mathrm{y}~ N(Bx_i,\Sigma),i=1,2\ldots,N$, and
$\mathrm{y}~N(B\theta, \Sigma)$ be independent multivariate observations, where
the $x_i$'s are known vectors, $B,\theta$ and $\Sigma$ are unknown, $\Sigma$
being a positive definite matrix. The calibration problem deals with
statistical inference concerning $\theta$ and the problem that we have
addressed is the construction of confidence regions. In this article, we have
constructed a region for $\theta$ based on a criterion similar to that
satisfied by a tolerance region. The situation where $\theta$ is possibly a
nonlinear function, say $\mathrm{h}(\xi)$ of fewer unknown parameters denoted
by the vector $(\xi)$, is also considered. The problem addressed in this
context is the construction of a region for $\xi$. The numerical computations
required for the practical implementation of our region are explained in detail
and illustrated using an example. Limited numerical results indicate that our
regions satisfy the coverage probability requirements of multipleuse
confidence regions.