We construct two variants of coarse-grained models of three hexaoses: one based on the centers of mass of the monomers and the other associated with the C4 atoms. The latter is found to be better defined and more suitable for studying interactions with proteins described within α-C based models. We determine the corresponding effective stiffness constants through all-atom simulations and two statistical methods. One method is the Boltzmann inversion (BI) and the other, named energy-based (EB), involves direct monitoring of energies as a function of the variables that define the stiffness potentials. The two methods are generally consistent in their account of the stiffness. We find that the elastic constants differ between the hexaoses and are noticeably different from those determined for the crystalline cellulose Iβ. The nonbonded couplings through hydrogen bonds between different sugar molecules are modeled by the Lennard-Jones potentials and are found to be stronger than the hydrogen bonds in proteins. We observe that the EB method agrees with other theoretical and experimental determinations of the nonbonded parameters much better than BI. We then consider the hexaose-Man5B catalytic complexes and determine the contact energies between their the C4α-C atoms. These interactions are found to be stronger than the proteinic hydrogen bonds: about four times as strong for cellohexaose and two times for mannohexaose. The fluctuational dynamics of the coarse-grained complexes are found to be compatible with previous all-atom studies by Bernardi et al.