We combine experimental and theoretical methods to assess the effect of a set of point mutations on c7A, a highly mechanostable type I cohesin module from scaffoldin CipA from Clostridium thermocellum. We propose a novel robust and computationally expedient theoretical method to determine the effects of point mutations on protein structure and stability. We use all-atom simulations to predict structural shifts with respect to the native protein and then analyze the mutants using a coarse-grained model. We examine transitions in contacts between residues and find that changes in the contact map usually involve a non-local component that can extend up to 50 Å. We have identified mutations that may lead to a substantial increase in mechanical and thermodynamic stabilities by making systematic substitutions into alanine and phenylalanine in c7A. Experimental measurements of the mechanical stability and circular dichroism data agree qualitatively with the predictions provided the thermal stability is calculated using only the contacts within the secondary structures.