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

It's formula is simply:

$$(\sum_{i=1}^n w_i)^{-1}(\sum_{i=1}e_i^2w_i)$$ 

where $e_i$ ($w_i$) is the residual (weight) (from the MM fit) associated with 
the $i^{th}$ observation.