Shielding for space microelectronics needs to provide an acceptable dose rate with minimum shield mass. The analysis presented here shows that the best approach is, in general, to use a graded-Z shield, with a high-Z layer sandwiched between two low-Z materials. A graded-Z shield is shown to reduce the electron dose rate by more than sixty percent over a single-material shield of the same areal density. For protons, the optimal shield would consist of a single, low-Z material layer. However, it is shown that a graded-Z shield is nearly as effective as a single-material shield, as long as a low-Z layer is located adjacent to the microelectronics. A specific shield design depends upon the details of the radiation environment, system model, design margins/levels, compatibility of shield materials, etc. Therefore, we present here general principles for designing effective shields and describe how the computer codes are used for this application.