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Obtaining precise theoretical predictions for both production and decay processes of heavy new particles is of great importance to constrain the allowed parameter spaces of Beyond-the-Standard-Model (BSM) theories, and to properly assess the sensitivity for discoveries and for discriminating between different possible BSM scenarios. In this context, it is well known that large logarithmic corrections can appear in the presence of widely separated mass scales. We point out the existence of a new type of possible large, Sudakov-like, logarithms in external-leg corrections of heavy scalars. To the difference of usual Sudakov logarithms, these can furthermore potentially be enhanced by large trilinear couplings. Such large logarithms are associated with infrared singularities and we review several techniques to address these at one loop. In addition to this discussion, we also present the derivation of the two-loop corrections containing this type of large logarithms, pointing out in this context the importance of adopting an on-shell renormalisation scheme. Finally, we illustrate our calculations and examine the possible magnitude of these corrections for a simple scalar toy model as well as for decay processes involving heavy stop quarks in the Minimal Supersymmetric Standard Model and a heavy Higgs boson in the Next-to-Two-Higgs-Doublet Model.