First-principles calculations of solids close to mechanical instabilities, for example, in studies of martensitic transformations in shape-memory alloys, require careful convergence with respect to both supercell size and k-point sampling density. Naturally, any such simulation should employ well-converged parameters that allow one to capture the quantitatively correct energetics of the most important instability waves. We demonstrate that large supercells used in Ab Initio Molecular Dynamics (AIMD) with common but insufficient k-point sampling can also produce qualitatively incorrect predictions of mechanical stability. A simple but useful rule is suggested: the most important destabilizing wave is identified, the smallest preferably uniformly spaced supercell allowing for such a wave is taken, for which k-points are converged; then a general scaling relation for maintaining equivalent k-point density across different supercell sizes stating that the number of k-points should scale with the inverse cube root of the number of primitive cells in the supercell is used. We validate this approach considering high-temperature shape-memory alloy NbRu, in which accurate prediction of a mechanical instability is crucial for modeling the martensitic transition. Using the most important 〈110〉[11̄0] destabilizing wave in B2-structured NbRu we show that a typical in AIMD studies Γ-point sampling alone for a 128-atom or even a 432-atom supercell cannot correctly predict stability against the wave that drives the martensitic transition, whereas the parameters for convergence can be easily estimated, and the properly converged calculations exhibit the correct behavior. These findings have direct implications for computational materials design involving large-scale, time-conserving simulations, particularly for systems in which mechanical instabilities govern functional properties.