In particle accelerators, the impedance of vacuum components is an important cause of beam instabilities. Smaller emittance is required in the new generation storage-ring-based light source, where smaller vacuum chamber is needed and the impedances are increased correspondingly.Therefore, the impedance of the vacuum components should be evaluated accurately and well optimized during the design stage. Impedance measurement is an important way to check the impedance model. The coaxial wire method is commonly used for laboratory bending measurements. For small-aperture vacuum components, the measurement error caused by the inner conductor is studied in this paper. For narrow-band impedances, pillbox cavity is used to study the influence of different inner conductor radius on the measurement results. As benchmarks, different numerical simulations, such as wake field, scattering parameters and eigenmodes, are carried out. The results show that the simulations are in good agreement with the measurement. It is also found that there exist deviations between the measurement and the existing theories on the dependence of the resonant frequency shift on the inner conductor radius. For non-narrowband impedances, we measured the impedance of a strip line kicker and studied the influence of the inner conductor, which verified the validity of the coaxial wire method.