Previous studies have shown that a specialized speech enhancement model can outperform a general model when the test condition is matched to the training condition. Therefore, choosing the correct (matched) candidate model from a set of ensemble models is critical to achieve generalizability. Although the best decision criterion should be based directly on the evaluation metric, the need for a clean reference makes it impractical for employment. In this paper, we propose a novel specialized speech enhancement model selection (SSEMS) approach that applies a non-intrusive quality estimation model, termed Quality-Net, to solve this problem. Experimental results first confirm the effectiveness of the proposed SSEMS approach. Moreover, we observe that the correctness of Quality-Net in choosing the most suitable model increases as input noisy SNR increases, and thus the results of the proposed systems outperform another auto-encoder-based model selection and a general model, particularly under high SNR conditions.