In the best case, where the minimum is far from any limits, Minuit will correctly transform the error matrix, and the parameter errors it reports should be accurate and very close to those you would have got without limits. In other cases (which should be more common, since otherwise you wouldn't need limits), the very meaning of parameter errors becomes problematic. Mathematically, since the limit is an absolute constraint on the parameter, a parameter at its limit has no error, at least in one direction. The error matrix, which can assign only symmetric errors, then becomes essentially meaningless. On the other hand, the [MINOs]MINOS analysis is still meaningful, at least in principle, as long as [MIGrad]MIGRAD (which is called internally by [MINOs]MINOS) does not get blocked at a limit. Unfortunately, the user has no control over this aspect of the [MINOs]MINOS calculation, although it is possible to get enough printout from the [MINOs]MINOS command to be able to determine whether the results are reliable or not.