Small and medium-sized enterprises (SMEs) play a fundamental role in aggregating scientific and technological talent, transforming technological achievements, and stimulating regional economic vitality. Well-designed government innovation honor incentives are crucial for achieving a “dual enhancement in both quantity and quality” of their innovation capabilities. Using the conferral of the China Patent Award-a concrete form of government innovation honor-as a quasi-natural experiment, this study constructs a multi-period difference-in-differences (DID) model with a sample of listed companies on China’s SME Board and ChiNext Market from 2008 to 2022, systematically revealing the asymmetric mechanism through which government innovation honors affect SMEs’ innovation capabilities. Empirical results show that government innovation honors significantly increase the quantity of innovation—primarily strategic innovation—by promoting the restructuring of cooperation networks and reducing corporate risk appetite. However, constrained by delays in knowledge network restructuring and resource misallocation following the alleviation of financing constraints, such honors inhibit innovation quality. Heterogeneity analysis reveals that this asymmetric effect is more pronounced among SMEs located in high-level administrative cities, those in competitive industries, and non-state-owned enterprises. Further extended discussion reveals that government innovation honors of different efficacy levels produce differentiated policy effects, while such honor incentives also exhibit significant cumulative effects and positive spillover characteristics. This study aims to provide theoretical foundations and empirical evidence for the ongoing improvement of the government-led innovation honor incentive system.