  For $r,n\ge2$, an ordered $r$-uniform matching $M^{(r)}_n$ of size $n$ is an
$r$-uniform hypergraph on a linearly ordered vertex set $V$, with $|V|=rn$,
consisting of $n$ pairwise disjoint edges. There are $\tfrac12\binom{2r}r$
different $M_2^{(r)}$'s, that is, different ways two edges may intertwine,
called here patterns. Among them we identify $3^{r-1}$ collectable patterns
$P$, which have the potential of appearing in arbitrarily large quantities
called $P$-cliques.
  We prove an Erd\H{o}s-Szekeres type result guaranteeing in every $M^{(r)}_n$
the presence of a $P$-clique of a prescribed size, for some collectable pattern
$P$. In particular, in the diagonal case, one of the $P$-cliques must be of
size $\Omega\left( n^{3^{1-r}}\right)$. In addition, for each collectable
pattern $P$ we show that the largest size of a $P$-clique in a \emph{random}
$M^{(r)}_n$ is, with high probability, $\Theta\left(n^{1/r}\right)$.
