  Motivated by deformation quantization, we consider in this paper
$^*$-algebras $\mathcal A$ over rings $\ring C = \ring{R}(i)$, where $\ring R$
is an ordered ring and $i^2 = -1$, and study the deformation theory of
projective modules over these algebras carrying the additional structure of a
(positive) $\mathcal A$-valued inner product. For $A=C^\infty(M)$, M a
manifold, these modules can be identified with Hermitian vector bundles E over
M. We show that for a fixed Hermitian star-product on M, these modules can
always be deformed in a unique way, up to (isometric) equivalence. We observe
that there is a natural bijection between the sets of equivalence classes of
local Hermitian deformations of $C^\infty(M)$ and $\Gamma^\infty(\End(E))$ and
that the corresponding deformed algebras are formally Morita equivalent, an
algebraic generalization of strong Morita equivalence of $C^*$-algebras. We
also discuss the semi-classical geometry arising from these deformations.
