This paper presents two new methods, space mapping (SM) with prior knowledge input (PKI-D) with difference and compound space mapping-based neuromodeling. Both methods combine two powerful techniques, space mapping-based neuromodeling and PKI-D with difference. The knowledge-based modeling methods in the RF/microwave literature merge the prior knowledge about the device to be modeled with neural network structures while a knowledge-based method, SP, focuses on reducing the computational burden. The main advantage of the proposed methods over these already existing knowledge-based methods are their better extrapolation capability and reduced number of training set data. The simulation results obtained reveal that both methods decrease the cost of training and improve the extrapolation capability and output performance of the SP-based neuromodeling. Copyright (c) 2007 John Wiley & Sons, Ltd.