This paper aims at the proposition of novel architectures for radial basis function neural networks implementation on hardware with custom-precision floating-point operations for black-box system modeling. An analysis tool was built to establish the trade-off between the consumption of hardware resources and the precision of the outputs, on the basis of the usage of the logic blocks on a field-programmable gate array and output quality. The architectures have been tested with a standard system identification benchmark and the speedup factors, when compared to a C implementation, are on the order of hundreds, what shows the importance of ad-hoc hardware architectures for improving computational efficiency.