The Wards actually cross streams and rivers on arched bridges. There as elsewhere, the essence of the Ward is a three-stone-high wall. It’s held up by the arches when it’s being built but once the Change is made, you could demolish the arches and the unbreakable wall would stay hovering like a ribbon across the water.
As elsewhere, no weapons, aetherial blood, or flesh Changed by Theurgy can pass either over or under the Ward. The river water can flow underneath just fine, as can vessels not carrying contraband of the above kinds.
As you may see in Grand Shayard, any riverboats of this kind are routinely searched by their owners for blades and other weapons before any journey. Otherwise you can easily end up with 90% of your boat stuck on one side of the Ward and no way to extract a knife from the other 10% without dismantling it. Simple, open barges and rafts are thus almost the only craft to traverse the Wards by river; for more elaborate vessels it would be too easy for a rival to sabotage it by sneaking a blade into the lower decks.