This article presents the frequency response of a surface acoustic wave (SAW) sensor for current measurements. The SAW sensor exploits the Love waves of a magnetostrictively coated delay line. The focus of this article lies on the frequency response of the sensor, which shows a very wide bandwidth. The delay time τD is the time an acoustic wave needs to traverse the delay line. Since the acoustic wave is modulated during the whole duration of the delay line crossing, τD is comparable to the integration time of a sample-and-hold device. The signal measured with the SAW sensor is averaged over the delay time. Therefore, undersampling behavior occurs for signal frequencies approaching 1/τD. A mathematical model of their frequency response up to several megahertz was developed and compared with measurements of two SAW sensors with different delay line lengths.