This paper analyses the possibility of damaging and destroying an identification chip of the Mifare type in a frequently used contactless identification card of size ID-1, following the standard ISO/IEC 7810 (i.e., with dimensions 85.60 × 53.98 × 0.76 mm), using the magnetic field of an adjacent conductor in which a current pulse of a defined shape and amplitude is flowing. For analysis purposes, the nonlinear current–voltage characteristic of the Mifare chip voltage limiter was measured and approximated, and the mutual inductance of the straight conductor and the rectangle coil antenna in the card was calculated. Next, a mathematical analysis was conducted based on the description of the equivalent electrical circuit by the differential equations. The results of the mathematical analysis were verified by a simulation in the free simulation software Micro-Cap 12. The peak value of the current pulse that can damage the Mifare chip was measured by a combination wave generator. Based on these measurements and the chip characteristics, the energy capable of destroying the chip was calculated. The characteristics of chip damage were determined using a comparison of the resonant characteristics of undamaged and damaged RFID cards with Mifare chips.