  We implement the Numerical Unified Transform Method to solve the Nonlinear
Schr\"odinger equation on the half-line. For so-called linearizable boundary
conditions, the method solves the half-line problems with comparable complexity
as the Numerical Inverse Scattering Transform solves whole-line problems. In
particular, the method computes the solution at any $x$ and $t$ without spatial
discretization or time stepping. Contour deformations based on the method of
nonlinear steepest descent are used so that the method's computational cost
does not increase for large $x,t$ and the method is more accurate as $x,t$
increase. Our ideas also apply to some cases where the boundary conditions are
not linearizable.
