A long time ago a used a software named MISAT which is applied to identify the best mutation model of a specific micro satellite locus. It may help you...
I think you need to specify more precisely what type of estimate you are looking for.
For example, any coalescent-based approach (e.g. simcoal) will allow to produce an estimate of a mutation parameter in terms of 4Nu (N for effective population size and u for mutation rate per gene per generation). This kind of mutation parameter can be estimated based on typical gen pop data (genotypes sampled within several populations). Assuming a given mutation model (SMM or TPM in the case of msats), and only then, you will be able to estimate 4Nu using one of several alternative estimators. Note, however, that 4Nu will refer to historical mutation rate (or an average across a coalescent process for a sample).
On the other hand, you may be interested in mutation rate alone (u as a separate parameter). In this case, but I am not an expert in the field, you would need large family data (parents and offspring) to infer u. A resulting mutation rate (u) will refer more to a contemporary mutation rate.
1- As evidenced by its name, MIGRATE estimates migration rates (not mutation rates). You could estimate mutation rates with LAMARC (http://evolution.genetics.washington.edu/lamarc/index.html)
2- Igor's response is a much better option, as LAMARC is too much dependant on the assumed historical and demographic models. However, I think you should complement the coalescent-based approach with a test of the best values that produce results closer to your observed data. For this, you need an ABC approach (for example, DIYABC). http://www1.montpellier.inra.fr/CBGP/diyabc/