A study of label-free silicon nitride asymmetric double-microring resonators is presented. The use of highly accurate 3D vector modal techniques permits an extensive exploration of the parameter space defining the architecture of the proposed device in the search for optimal geometries and reaching configurations not addressed in previous studies that had been limited to symmetrical configurations. Asymmetry, on the other hand, permits to access resonances that exploit the radiation-quenching properties of the structure in an optimal way. The analysis presented also includes the effect of absorption in the sensor aqueous cladding that is generally omitted. The results of the numerical survey indicate that the optimized geometries bring about a substantive performance improvement at small microring radii that are impractical for more conventional single-ring geometries due to the high radiation losses. Therefore, lower footprint devices, and a larger scale of integration, can be attained with the proposed structure.