Coarse-grained (CG) modeling is a promising way to study materials with chemical detail with a computer at minimal computational cost. Accurate and reliable CG simulation could speed-up the research and development process for the design for pharmaceuticals, tires, batteries, etc. Also, they offer the opportunity to test hypotheses with molecular resolution. However, there are several issues that must first be addressed in order to make CG modeling truly practical. Key among these is transferability and representability. In this thesis, work is presented that addresses aspects of transferability and representability. First, an approach is presented to calculate the sensitivity of coarse-grained models to changes in the model from which they are derived. This sensitivity can be used to compute first order corrections to CG interactions that extend the range over which CG models can accurately be transferred. Second, an approach is discussed that would allow one to construct CG observables that reproduce the observables of the model from which the CG model is derived. Then, a method to implement this approach is presented. Third, a new class of interactions is introduced that allows CG models to more faithfully reproduce features of the model from which it is derived. Different terms in this class are implemented and applied to liquids at interfaces as well as a protein system. Taken together, this work provides a way to further improve the transferability and representability of CG models.