In this article a task-oriented neural network (NN) solution is proposed for the problem of article recovering real process outputs from available distorted measurements. It is shown that a neural network can be used as approximator of inverted first-order measurement dynamics with and without time delay. The trained NN is connected in series with the sensor, resulting in an identity mapping between the inputs and the outputs of the composed system. In this way the network acts as a software mechanism to compensate for the existing dynamics of the whole measurement system and recover the actual process output. For those cases where changes in the measurement system occur, a multiple concurrent-NN recovering scheme is proposed. This requires a periodical path-finding calibration to be performed. A procedure for such a calibration purpose has also been developed, implemented, and tested. It is shown that it brings adequate robustness to the overall compensation scheme. Results showing the performance of both the NN compensator and the calibration procedure are presented for closed loop system operation.