Estimate scale parameter from 5% contaminated mean-zero normal sample

Question

I have a normal sample but that is contaminated in the left and the right tails (no more than 2.5% each). The contamination gives rise to high and low values. I wanted to know what methods I have in order to estimate ths sigma of the N(0, sigma^2) distribution. I have looked at R's vignettes but almost all the examples there are on different aspects of linear and other models. I am looking for a simple estimate of the scale parameter of the distribution in the presence of at most 5% contaminants. I can use something crude like 1.5 times median of the absolute values of the inner 95% but I was wanting something more precise and specific. Any suggestions? Thanks in advance for any help!