For regulating and presetting the pump rate of a blood pump, a device and a method are configured for monitoring blood pressure values upstream and/or downstream from the blood pump. The monitored values, or another value formed from the monitored values, are compared with a limit value, which depends on an operating parameter or a pump parameter of the blood pump. In violation of the limit value, the pump rate of the blood pump is modified to such an extent, or a new pump rate is determined, such that the limit value is no longer violated or the degree of violation is reduced.