A matrix congruence \(\sigma\) on a semigroup S is a congruence for which S/\(\sigma\) is a rectangular band. In this paper, the author presents conditions by which a matrix congruence on the band \(E_ S\) of idempotents of an orthodox semigroup S can be extended to a matrix congruence on S. In particular, for an orthodox semigroup S it is shown that if the least matrix congruence on \(E_ S\) can be extended to a matrix congruence on S then every matrix congruence on \(E_ S\) can be also extended to a matrix congruence on S. Further, the following results are given. (1) Let S be a generalized inverse semigroup satisfying the following condition: For all \(a\in S\), there exists an inverse a' of a and an idempotent g such that \(g\leq aa'\) and \(g\leq a'a\). Then, every matrix congruence on \(E_ S\) can be uniquely extended to a matrix congruence on S. (2) If S is an orthodox semigroup which is a matrix of inverse semigroups then the least matrix congruence on \(E_ S\) can be extended to a matrix congruence on S.