Noise caused by the electromagnetic coupling of digitally injected signals into substrate is a key problem in the design of large mixed-signal circuits. This paper describes methods which allow the circuit designers to efficiently model such substrate noise in large mixed-signal SPICE designs. With the help of these techniques a new methodology is developed for efficiently modelling the current injected electromagnetic noise in the substrate and its coupling to analogue signals. The new method is then extended to provide real time modelling capability. The practicality and the numerical efficiency of the methods are demonstrated on several example circuits.