This study presents a noncontact measurement of biological tissues with the elimination of curved-surface air gap using a triple-ring complementary split-ring resonator (CSRR). The resonance frequency deviations are accessed to measure the thickness of the material under test (MUT), with multiple estimations to reduce the errors. An equivalent mapping is proposed to convert the curved-surface boundary to a simplified uniform air-gap method. The accuracy of the thickness measurement of the MUT improves under the existence of unknown curved air gap. This paper proposes a low-cost CSRR to measure the thickness of a curved porcine fat. The average absolute errors of measured results of a 3-mm porcine fat is 1.43 mm, which is acceptable for a lossy curved, rough-surfaced material. The provided technique shows an excellent solution of eliminating the influence of non-planar surface on measurement.