It is well established that trehalose (TRH) affects the physical properties of lipid bilayers and stabilizes biological membranes. We present molecular dynamics (MD) computer simulations to investigate the interactions between lipid membranes formed by 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and TRH. Both atomistic and coarse-grained (CG) interaction models were employed, and the coarse graining of DMPC leads to a reduction in the acyl chain length corresponding to a 1,2-dilauroyl-sn-glycero-3-phosphocholine lipid (DLPC). Several modifications of the Martini interaction model, used for CG simulations, were implemented, resulting in different potentials of mean force (PMFs) for DMPC bilayer TRH interactions. These PMFs were subsequently used in a simple two-site analytical model for the description of sugar binding at the membrane interface. In contrast to that in atomistic MD simulations, the binding in the CG model was not in agreement with the two-site model. Our interpretation is that the interaction balance, involving water, TRH, and lipids, in the CG systems needs further tuning of the force-field parameters. The area per lipid is only weakly affected by TRH concentration, whereas the compressibility modulus related to the fluctuations of the membrane increases with an increase in TRH content. In agreement with experimental findings, the bending modulus is not affected by the inclusion of TRH. The important aspects of lipid bilayer interactions with biomolecules are membrane curvature generation and sensing. In the present investigation, membrane curvature is generated by artificial buckling of the bilayer in one dimension. It turns out that TRH prefers the regions with the highest curvature, which enables the most favorable situation for lipid sugar interactions.