This paper proposes a novel palpable and non-invasive continuous sphygmomanometer, with which continuous arterial pressure can be measured based on electromagnetic induction. The proposed sensor can be attached to the measurer's fingertip, and single-degree-of-freedom springs, which are interposed between the side of the measurer's finger and the skin surface side, transmit the arterial pressure to the measurer. At the same time, displacements of the springs are measured by electromagnetic induction, and converted into a measurement of arterial pressure. This mechanism allows measurement of the continuous arterial pressure based on a tonometry approach. In the experiment, the conversion equations from the output voltage to arterial pressure values were verified by comparison with the arterial pressure measured using a commercial continuous sphygmomanometer. The experimental results showed that the determination coefficient of the regression line between arterial pressures measured using the sensors was 0.89 (p < 0.01). Therefore we can conclude that the proposed sensor enables the non-invasive measurement of continuous arterial pressure.