the robust scale is normally outputed by the routine you used to estimate the MM. 
For example in R:

    library(robustbase)
    data(coleman)
    set.seed(0)
    RlmST <- lmrob(log.light ~ log.Te, data = starsCYG)
    RlmST$scale


There is no explicit formula to compute it: it's the result 
of an iterative