In this work, we propose and examine two procedures for constructing intervals that capture the uncertainty associated with determining the effective number of components in model selection problems. The output of these methods is an interval (defined by two integer bounds) representing plausible values for the number of components. A detailed discussion is provided on the connection between the proposed approaches andthe widely-used information criteria in the literature. Notably, the methods do not relyon the availability of a likelihood function, making them broadly applicable across variousdomains such as regression, classification, feature and/or order selection, clustering, anddimensionality reduction. These techniques leverage geometric properties of the error curve to construct the intervals. Extensive experiments on both synthetic and real-world datasets demonstrate the effectiveness and practical utility of the proposed procedures. Additionally, MATLAB code is provided to facilitate adoption by practitioners and researchers.