Let L be a congruence-uniform lattice. In this article, we investigate the shard order on L that was introduced by N. Reading. When L can be realized as a poset of regions of a hyperplane arrangement the shard order is always a lattice. For general L, however, this fails. We provide a necessary condition for the shard order to be a lattice, and we show how to construct a congruence-uniform lattice L⁰ from L such that the shard order on L⁰ fails to be a lattice.