Creating time-marching unsteady governing equations for a steady state in high-speed flows is not a trivial task. Residue convergence in time cannot be achieved when using most low- and high-order spatial discretization schemes. Recently, high-order, weighted, essentially non-oscillatory schemes have been specially designed for steady-state simulations. They have been shown to be capable of achieving machine precision residues when simulating the Euler equations under canonical coordinates. In the present work, we review these schemes and show that they can also achieve machine residues when simulating the Navier–Stokes equations under generalized coordinates. This is carried out by considering three supersonic flows of perfect fluids, namely the flow upstream a cylinder, the flow over a blunt wedge, and the flow over a compression ramp.