State estimation is a widely used concept in the control community, and the literature mostly concentrates on the estimation of all states. However, in soft sensor problems, the emphasis is on estimating a few soft outputs as accurately as possible. The concept of preferential estimation consists of estimating these soft outputs with an accuracy higher than those with which the other states are estimated. The main question is whether or not the accuracy along the soft outputs can be improved at the detriment of others. This papers shows that, though preferential estimation is not possible for ideal linear systems, it is indeed possible for linear systems with model uncertainty. The theoretical concepts are illustrated on a filamentous fungal fermentation.