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This paper proposes a new approach to estimating multipath parameters such as time delays and attenuation factors for channel measurements using a vector network analyzer. In the proposed scheme, we introduce a coarse-and-fine time-delay-estimation scheme and attenuation-factor-estimation schemes. The coarse time-delay estimation employs a superresolution technique based on the generalized eigenvalues utilizing signal subspace eigenvectors (GEESE) algorithm, and the fine time-delay estimation is derived to exploit real-valued attenuation factors. For attenuation-factor estimation, we focus on the least squares estimator (LSE) and the simplified estimator (SE). Numerical results show that the proposed time-delay-estimation scheme outperforms the multiple-signal classification (MUSIC)-based time-delay-estimation scheme. Theoretical analysis and computer simulations are used in the comparisons of the LSE and the SE.