A nonlocal two-point boundary value problem is a system of ordinary differential equations in which the equations and/or the boundary conditions contain terms or coefficients that depend on an integral of a function that depends on one of the solution components. We discuss the reformulation of nonlocal two-point boundary problems to enable their approximate solution using widely available software packages that provide a continuous numerical approximation to a user-prescribed accuracy. One such package, COLNEWSC, is used to solve a collection of problems from the literature, and comparisons are made with results that have been obtained using published methods. We show that, using the reformulation approach, these problems can be solved simply and efficiently to almost machine accuracy.