This paper deals with the possibility of adopting microwave imaging to continuously monitor a patient after the onset of a brain stroke, with the aim to follow the evolution of the disease, promptly counteract its uncontrolled growth, and possibly support decisions in the clinical treatment. In such a framework, the assessed techniques for brain stroke diagnosis are indeed not suitable to pursue this goal. Conversely, microwave imaging can provide a diagnostic tool able to follow up the disease’s evolution, while relying on a relatively low cost and portable apparatus. The proposed imaging procedure is based on a differential approach which requires the processing of scattered field data measured at different time instants. By means of a numerical analysis dealing with synthetic data generated for realistic anthropomorphic phantoms, we address some crucial issues for the method’s effectiveness. In particular, we discuss the role of patient-specific information and the effect of inaccuracies in the measurement procedure, such as an incorrect positioning of the probes between two different examinations. The observed results show that the proposed technique is indeed feasible, even when a simple, nonspecific model of the head is exploited and is robust against the above mentioned inaccuracies.