The advent of transesophageal ultrasound robots has provided a new idea to simplify relevant clinical procedures. However, the existing add-on robots often lack the ability to predict the contact force between the probe tip and the tissue. This makes the control of this robot under teleoperation lacking in tactile feedback and difficult to obtain effective safety. In this study, we propose a neural network-based internal resistance modeling method. Based on this, we experimentally calibrated the relationship between the tip contact force and handwheel torque through a self-learning idea. The experimental results show that a microcontroller-deployable lightweight neural network can achieve a good result on the fitting of the internal resistance, with its standard deviation being less than 3%. Moreover, a good linear correlation between the tip contact force and the handwheel torque was demonstrated in the case of passively applied forces. Independent experiments with actively applied forces further demonstrated the feasibility of the prediction method, especially in the forward bending process, with the prediction error mostly within 20% of the baseline force. Therefore, we believe that the proposed method has good potential to improve the safe use of transesophageal ultrasound robots.