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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 quantitiescalled $P$-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 ofsize $\Omega\left( n^{3^{1-r}}\right)$. In addition, for each collectablepattern $P$ we show that the largest size of a $P$-clique in a \emph{random}$M^{(r)}_n$ is, with high probability, $\Theta\left(n^{1/r}\right)$.

Erd\H{o}s-Szekeres type Theorems for ordered uniform matchings