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Nonlinear optical effects have been studied extensively in microresonators as more photonics applications transitions to integrated on-chip platforms. Due to low optical losses and small mode volumes, microresonators are demonstrably the state-of-the-art platform for second-harmonic generation (SHG). However, the working bandwidth of such microresonator-based devices is relatively small, presenting a challenge for applications where a specifically targeted wavelength needs to be addressed. In this Letter, we analyze the phase-matching window and resonance wavelength with respect to varying microring widths, radii, and temperatures. A chip with precise design parameters was fabricated with phase matching realized at the exact wavelength of a two-photon transition of Rb85. This procedure can be generalized to any target pump wavelength in the telecom band with picometer precision.