I am doing a couple of coaching jobs, one being the typical blank slate landscaping job and the other can you believe is a swale. Unbeknown to most gardeners, swale gardening is a whole other area of expertise. I am certainly not an expert but I did have a swale in my last home.
Just because there is a graduated dip so the water will flow into this area and away does not mean it is always wet. The banks of the swale can be quite dry, but eventually the roots from these fringe plants will reach down into where the water flows. I had three River Birches which loved the wet conditions, banks planted in day lilies which will also tolerate some wetness, some Red Barbary, Claveys Dwarf Honeysuckle and Cranberry Viburnums. They all did very well with the only planting at the bottom of the swale being the River Birch.
The garden I have looked at had to do a swale because water was leaking into their windrow wells and subsequently their foundation and basement. I am thinking just because of the size of our lots, River Birch trees will not be an option. So we talked about some plantings, Carex Ice Fountains (for the shady, wet area overshadowed by large arborvitaes), Viburnum Autumn Jazz in the sunnier area with plantings of daylilies below. In the front area of the swale it is also sunny (with three Green Mountain Boxwood already planted), so I suggested coneflowers White Swan and Kim's Knee High. At the back end leading into the back garden where the swale has ended, it would be nice to end the walk with Viburnum Carlesi Compactum. All of the large fieldstones will need to be relaid because they are on a slant. Not all of the plantings will be "in" the swale but will border it on top and bottom.
The main goal with a swale is to hold the soil on the sides. My present yard had a really dangerous swale when we moved in: whereas; you had to step down from the patio to walk to the front of the yard, there was no gradual descent. We had a raised bed built and a paver walkway put from back to front gradually maintaining the swale. In most cases you cannot remove this swale without impacting neighboring property or your own.