  An ordered $r$-matching of size $n$ is an $r$-uniform hypergraph on a
linearly ordered set of vertices, consisting of $n$ pairwise disjoint edges.
Two ordered $r$-matchings are isomorphic if there is an order-preserving
isomorphism between them. A pair of twins in an ordered $r$-matching is formed
by two vertex disjoint isomorphic sub-matchings. Let $t^{(r)}(n)$ denote the
maximum size of twins one may find in every ordered $r$-matching of size $n$.
  By relating the problem to that of largest twins in permutations and applying
some recent Erd\H{o}s-Szekeres-type results for ordered matchings, we show that
$t^{(r)}(n)=\Omega\left(n^{\frac{3}{5\cdot(2^{r-1}-1)}}\right)$ for every fixed
$r\geqslant 2$. On the other hand,
$t^{(r)}(n)=O\left(n^{\frac{2}{r+1}}\right)$, by a simple probabilistic
argument. As our main result, we prove that, for almost all ordered
$r$-matchings of size $n$, the size of the largest twins achieves this bound.
