In typical MRI applications the dominant noise sources in the received signal are the sample, the coil loop and the preamplifier. We hypothesize that in some cases (e.g. for very small receiver coils) the matching network noise has to be considered explicitly. Considering the difficulties of direct experimental determinations of the noise factor of matching networks with sufficient accuracy, it is helpful to estimate the noise factor by calculation. A useful formula of the coil matching network is obtained by separating commonly used coil matching network into different stages and calculating their noise factor analytically by a combination of the noise from these stages. A useful formula of the coil matching network is obtained. ADS simulations are performed to verify the theoretical predictions. Thereafter carefully-designed proof-of-concept phantom experiments are carried out to qualitatively confirm the predicted SNR behavior. The matching network noise behavior is further theoretically investigated for a variety of scenarios. It is found that in practice the coil matching network noise can be improved by adjusting the coil open port resonant frequency.