Non-detectable (ND) and outlying concentration values (OV) are a common challenge of biomarker investigations. However, best practices on how to aptly deal with the affected cases are still missing. The high methodological heterogeneity in biomarker-oriented research, as for example, in the field of psychoneuroendocrinology, and the statistical bias in some of the applied methods may compromise the robustness, comparability, and generalizability of research findings. In this paper, we describe the occurrence of ND and OV in terms of a model that considers them as censored data, for instance due to measurement error cutoffs. We then present common univariate approaches in handling ND and OV by highlighting their respective strengths and drawbacks. In a simulation study with lognormal distributed data, we compare the performance of six selected methods, ranging from simple and commonly used to more sophisticated imputation procedures, in four scenarios with varying patterns of censored values as well as for a broad range of cutoffs. Especially deletion, but also fixed-value imputations bear a high risk of biased and pseudo-precise parameter estimates. We also introduce censored regressions as a more sophisticated option for a direct modeling of the censored data. Our analyses demonstrate the impact of ND and OV handling methods on the results of biomarker-oriented research, supporting the need for transparent reporting and the implementation of best practices. In our simulations, the use of imputed data from the censored intervals of a fitted lognormal distribution shows preferable properties regarding our established criteria. We provide the algorithm for this favored routine for a direct application in R on the Open Science Framework (https://osf.io/spgtv). Further research is needed to evaluate the performance of the algorithm in various contexts, for example when the underlying assumptions do not hold. We conclude with recommendations and potential further improvements for the field.