As a resonator-based optical hardware in analog optical computing, a microring synapse can be straightforwardly configured to simulate the connection weights between neurons, but it faces challenges in precision and stability due to cross talk and environmental perturbations. Here, we propose and demonstrate a self-calibration scheme with dual-wavelength synchronization to monitor and calibrate the synaptic weights without interrupting the computation tasks. We design and fabricate an integrated 4×4 microring synapse and deploy our self-calibration scheme to validate its effectiveness. The precision and robustness are evaluated in the experiments with favorable performance, achieving 2-bit precision improvement and excellent robustness to environmental temperature fluctuations (the weights can be corrected within 1 s after temperature changes 0.5°C). Moreover, we demonstrate matrix inversion tasks based on Newton iterations beyond 7-bit precision using this microring synapse. Our scheme provides an accurate and real-time weight calibration independently parallel from computations and opens up new perspectives for precision boost solutions to large-scale analog optical computing.