Calcium-dependent heart muscle contraction is regulated by the cardiac troponin protein complex (cTn) and specifically by the N-terminal domain of its calcium binding subunit (cNTnC). cNTnC contains one calcium binding site (site II), and altered calcium binding in this site has been studied for decades. It has been previously shown that cNTnC mutants, which increase calcium sensitization may have therapeutic benefits, such as restoring cardiac muscle contractility and functionality post-myocardial infarction events. Here, we computationally characterized eight mutations for their potential effects on calcium binding affinity in site II of cNTnC. We utilized two distinct methods to estimate calcium binding: adaptive steered molecular dynamics (ASMD) and thermodynamic integration (TI). We observed a sensitizing trend for all mutations based on the employed ASMD methodology. The TI results showed excellent agreement with experimentally known calcium binding affinities in wild-type cNTnC. Based on the TI results, five mutants were predicted to increase calcium sensitivity in site II. This study presents an interesting comparison of the two computational methods, which have both been shown to be valuable tools in characterizing the impacts of calcium sensitivity in mutant cNTnC systems.