Deep Neural Networks (DNNs) face challenges during deployment due to covariate shift, i.e., data distribution shifts between development and deployment contexts. Fine-tuning adapts pre-trained models to new contexts requiring smaller labeled sets. However, testing fine-tuned models under constrained labeling budgets remains a critical challenge. This paper introduces MetaSel, a new approach tailored for DNN models that have been fine-tuned to address covariate shift, to select tests from unlabeled inputs. MetaSel assumes that fine-tuned and pre-trained models share related data distributions and exhibit similar behaviors for many inputs. However, their behaviors diverge within the input subspace where fine-tuning alters decision boundaries, making those inputs more prone to misclassification. Unlike general approaches that rely solely on the DNN model and its input set, MetaSel leverages information from both the fine-tuned and pre-trained models and their behavioral differences to estimate misclassification probability for unlabeled test inputs, enabling more effective test selection. Our extensive empirical evaluation, comparing MetaSel against 11 state-of-the-art approaches and involving 68 fine-tuned models across weak, medium, and strong distribution shifts, demonstrates that MetaSel consistently delivers significant improvements in Test Relative Coverage (TRC) over existing baselines, particularly under highly constrained labeling budgets. MetaSel shows average TRC improvements of 28.46% to 56.18% over the most frequent second-best baselines while maintaining a high TRC median and low variability. Our results confirm MetaSel's practicality, robustness, and cost-effectiveness for test selection in the context of fine-tuned models.