The possibility of applying CMR-B-scalar sensors made from thin manganite films exhibiting the colossal magnetoresistance effect as a fast-nondestructive method for the evaluation of the quality of the magnetic pulse welding (MPW) process is investigated in this paper. This method based on magnetic field magnitude measurements in the vicinity of the tools and joining parts was tested during the electromagnetic compression and MPW of an aluminum flyer tube with a steel parent. The testing setup used for the investigation allowed the simultaneous measurement of the flyer displacement, its velocity, and the magnitude of the magnetic field close to the flyer. The experimental results and simulations showed that, during the welding of the aluminum tube with the steel parent, the maximum magnetic field in the gap between the field shaper and the flyer is achieved much earlier than the maximum of the current pulse of the coil and that the first half-wave pulse of the magnetic field has two peaks. It was also found that the time instant of the minimum between these peaks depends on the charging energy of the capacitors and is associated with the collision of the flyer with the parent. Together with the first peak maximum and its time-position, this characteristic could be an indication of the welding quality. These results were confirmed by simultaneous measurements of the flyer displacement and velocity, as well as a numerical simulation of the magnetic field dynamics. The relationship between the peculiarities of the magnetic field pulse and the quality of the welding process is discussed. It was demonstrated that the proposed method of magnetic field measurement during magnetic pulse welding in combination with subsequent peel testing could be used as a nondestructive method for the monitoring of the quality of the welding process.