Creep rupture prediction for materials serving in fossil-fired power plants has been a critical issue for many decades. There are many empirical methods with several fitting or adjustable parameters that have been proposed for creep rupture strength prediction. Fundamental models based on the microstructure mechanism have been developed but are not widely used due to their complicated nature. Neural Network (NN) is a powerful tool for handling complicated mechanical behaviour; However, unexpected results and excessive errors can be generated. To avoid this, constraints on the first and second derivatives of the creep rupture curves have been introduced and combined with the NN. With the constrained NN models, extrapolated results with controlled errors can be obtained, which is verified by methods for error analysis. Furthermore, ECCC Post Assessment Tests (PATs) 1.1 to 2.2 are satisfied. The methods are illustrated for two creep-resistant austenitic steels Sanicro 25 and Super304H.