This work presents a method to quantitatively calculate the error induced through application of approximate boundary conditions in quantum charge transport simulations based on the Wigner transport equation (WTE). Except for the special case of homogeneous material, there exists no methodology for the calculation of exact boundary conditions. Consequently, boundary conditions are customarily approximated by equilibrium or near-equilibrium distributions known to be correct in the classical limit. This practice can, however, exert deleterious impact on the accuracy of numerical calculations and can even lead to unphysical results. The Yoder group has recently developed a series expansion for exact boundary conditions which, when truncated, can be used to calculate boundary conditions of successively greater accuracy through consideration of successively higher order terms, the computational penalty for which is however not to be underestimated. This thesis focuses on the calculation and analysis of the second order term of the series expansion. A method is demonstrated to calculate the term for any general device structure in one spatial dimension. In addition, numerical analysis is undertaken to directly compare the first and second order terms. Finally a method to incorporate the first order term into simulation is formulated.