We study the field enhancement and resonance frequencies in split-ring resonators (SRR) illuminated by azimuthally polarized light. We find that compared to linearly polarized illumination, the azimuthally polarized illumination increase the intensity enhancement by more than an order of magnitude. We attribute the increase in the intensity enhancement to the improved overlap between the SRR geometry and the direction of the electric field vector at each point. In addition, we present and explore a method to tune the resonance frequency of the SRR (for azimuthal polarization) by introducing more gaps in the structure. This approach allows for simple and straightforward tuning of the resonance frequency with small impact on the intensity enhancement. The impact of the design parameters on the intensity enhancement under azimuthally polarized illumination is also studied in details, exhibiting clear differences compared to the case of linear polarized illumination.