Corneal endothelial cell cultures have a tendency to undergo epithelial-to-mesenchymal transition (EMT) after loss of cell-to-cell contact. EMT is deleterious for the cells as it reduces their ability to form a mature and functional layer. Here, we present a method for establishing and subculturing human and sheep corneal endothelial cell cultures that minimizes the loss of cell-to-cell contact. Explants of corneal endothelium/Descemet's membrane are taken from donor corneas and placed into tissue culture under conditions that allow the cells to collectively migrate onto the culture surface. Once a culture has been established, the explants are transferred to fresh plates to initiate new cultures. Dispase II is used to gently lift clumps of cells off tissue culture plates for subculturing. Corneal endothelial cell cultures that have been established using this protocol are suitable for transferring to biomaterial membranes to produce tissue-engineered cell layers for transplantation in animal trials. A custom-made device for supporting biomaterial membranes during tissue culture is described and an example of a tissue-engineered graft composed of a layer of corneal endothelial cells and a layer of corneal stromal cells on either side of a collagen type I membrane is presented.