We present a general model of noisy scattering-parameter (S-parameter) measurements performed by a vector network analyzer (VNA). The residual error of the S-parameter due to the noise is examined to appear like a complex Gaussian quotient. The statistical analysis of the residual error is given, and relevant statistical quantities are derived and discussed. Experiments were conducted on a two-port VNA to validate the noise-influenced S-parameter model. We show that the uncertainty due to the noise is often critical in S-parameter measurements, in particular for S-parameters of a small magnitude.