In monitoring an isolation of an ungrounded power grid an AC voltage source is connected to the power grid via at least one test resistor. A test signal with a periodic continuous voltage course with regard to ground and with a frequency is applied to the power grid by means of the AC voltage source. A leakage current flowing due to the test signal is measured; and an ohmic isolation resistance is determined from the leakage current. The frequency of the test signal is varied such that an active current part of the leakage current keeps a predetermined recommended value at varying leakage capacitances of the power grid. This provides for a desired level of accuracy at maximum speed of isolation or ground fault detection.