This paper presents a novel approach for establishing microstructure statistics-property relations for a silver particle-based thermal interface material (TIM). Several sintered silver TIMs have been prepared under different processing conditions, generating samples with distinct microstructures. The 3D microstructure is revealed and visualized using the combination of Focussed Ion Beam (FIB) milling and Scanning Electron Microscopy (SEM) imaging. Representative synthetic model microstructures have been generated based on Gaussian random field models, having well defined analytical descriptions. The statistical characteristics of the samples and the synthetic models are shown to have a good correspondence, indicating that the linear effective properties of these complex materials can be predicted based on analytical estimates available for the synthetic models. This is verified by computing the effective elastic and thermal material properties using the computational homogenization approach based on the finite element models of the real samples. The computational homogenization, providing the reference solution, and the higher-order statistical estimates for the synthetic models are in very good agreement. These results can be used in the development of new silver particle-based materials, whereby the expensive and time consuming effective material property characterization can be replaced by efficient estimation based on the synthetic random field models.