The usage of electronic systems in safety-critical applications requires mechanisms for the early detection of faults affecting the hardware while the system is in the field. When the system includes a processor, one approach is to make use of functional test programs that are run by the processor itself. Such programs exercise the different parts of the system, and eventually expose the difference between a fully functional system and a faulty one. Their effectiveness depends, among other factors, on the mechanism adopted to observe the behavior of the system, which in turn is deeply affected by the constraints imposed by the application environment. This paper describes different mechanisms for supporting the observation of fault effects during such in-field functional test, and it reports and discusses the results of an experimental analysis performed on some representative case studies, which allow drawing some general conclusions. The gathered results allow the quantitative evaluation of the drop in fault coverage coming from the adoption of the alternative approaches with respect to the ideal case in which all the outputs can be continuously monitored, which is the typical scenario for test generation. The reader can thus better evaluate the advantages and disadvantages provided by each approach. As a major contribution, the paper shows that in the worst case the drop can be significant, while it can be minimized (without introducing any significant extra cost in terms of test generation and duration) through the adoption of a suitable observation mechanism, e.g., using Performance Counters possibly existing in the system. Suitable techniques to implement fault simulation campaigns to assess the effectiveness of different observation mechanisms are also described.