Nested cartesian grid systems by design require interpolation of solution fields from coarser to finer grid systems. While several choices are available, preserving accuracy, stability and efficiency at the same time require careful design of the interpolation schemes. Given this context, a series of interpolation algorithms based on post processing halo information on nested cartesian finite difference grids of different size were developed and tested. The results obtained indicate that most of these do not yield the expected improvement, and some even tend to make the solver unstable. However, some third and fourth order interpolation functions do yield considerable accuracy improvement, are stable, and are worth implementing.