We demonstrate the ability of a stabilized finite element method, inspired by the weighted Nitsche approach, to alleviate spurious traction oscillations at interlaminar interfaces during composite delamination. The method allows for the use of any value for the cohesive stiffness and obviates the need for ad hoc approaches to estimate the minimum penalty stiffness for accurate analysis. Simulation studies involving constant strain patch tests and benchmark delamination tests under mode-I, mode-II, and mixed-mode loadings show evidence of traction oscillations with the standard method. In contrast, the stabilized method is able to alleviate traction oscillations, which illustrates its efficacy and robustness. © 2021 Taylor & Francis Group, LLC.