In statistical analysis, the reliability of test procedures is crucial for accurate inference from the data. However, the presence of measurement errors in the data and model misspecification constitute important challenges that can lead to wrong conclusions. Robust methods aim to maintain reliability even under contamination, outliers, and misspecifications of the model. Kernel-Based Quadratic Distances (KBQDs) are efficient tools in nonparametric statistics and have been used for constructing goodness-of-fit tests. This research explores the robustness of KBQD tests for normality, evaluating their sensitivity in terms of level and power under data contamination. Through a simulation study, we illustrate the performance of these tests by assessing the trade-offs between sensitivity and robustness and reinforcing the need for more reliable and accurate statistical tests dealing with imperfect data.