We investigate the local optical response of split-ring resonator-(SRR)-based metamaterials with an apertureless scanning near-field optical microscope. By mapping the near fields of suitably resonant micrometer-sized SRRs in the near-infrared spectral region with an uncoated silicon tip, we obtain a spatial resolution of better than lambda/50. The experimental results confirm numerical predictions of the near-field excitations of SRRs. Combining experimental near-field optical studies with near- and far-field optical simulations provides a detailed understanding of resonance mechanisms in subwavelength structures and will facilitate an efficient approach to improved designs.