We address the computational and theoretical limitations of existing distributional alignment methods for unsupervised domain adaptation (UDA), particularly regarding the estimation of classification performance and confidence without target labels. Current theoretical frameworks for these methods often yield computationally intractable quantities and fail to adequately reflect the properties of the alignment algorithms employed. To overcome these challenges, we introduce the Optimal Transport (OT) score, a confidence metric derived from a novel theoretical analysis that exploits the flexibility of decision boundaries induced by Semi-Discrete Optimal Transport alignment. The proposed OT score is intuitively interpretable, theoretically rigorous, and computationally efficient. It provides principled uncertainty estimates for any given set of target pseudo-labels without requiring model retraining, and can flexibly adapt to varying degrees of available source information. Experimental results on standard UDA benchmarks demonstrate that classification accuracy consistently improves by identifying and removing low-confidence predictions, and that OT score significantly outperforms existing confidence metrics across diverse adaptation scenarios.