In this study we explore a systematic procedure to coarsen a microscopic model towards a mesoscopic model. The procedure is applied to a system of chains of ten beads, representing a low molecular weight polymer melt. Our method consists of defining coarse-grained sites in the microscopic system, and calculating their spatial distribution on the pair level. The effective interaction between the coarse-grained sites is then obtained by bringing the pair interaction in consistence with the pair density. We investigate both a dynamic and a stochastic method for this step. The so obtained mesoscopic interaction is used in a molecular dynamics simulation to investigate the pressure of the coarse-grained system. We found that the pair interaction that reproduces the pair density predicts a pressure that is significantly lower than the microscopic value, even if we take the state-dependency of the coarse-grained interactions into account. We therefore conclude that coarse-grained models lack thermodynamic consistency.