The problem of gap filling in the data from high-latitude magnetic stations, critical for ensuring the continuity of geophysical observations and space weather monitoring, is considered. The relevance of the study is due to the high dynamics of the geomagnetic field in the auroral zone, where traditional interpolation methods may be rather insufficient. A geostatistical approach to interpolation of minute values of the eastward geomagnetic field component based on ordinary kriging using the GSTools library is proposed. The method was tested on the SuperMAG network data from ten high-latitude stations for the period of 2019-2020 with the target one of Lovozero (LOZ). A comparative analysis of the kriging efficiency and the inverse distance weighting method for various gap durations and levels of geomagnetic activity, classified by the SME index, was made. We found out that the IDW method yields unsatisfactory results (negative R2 values), while kriging provides consistently positive ones: the coefficient of determination ranges from 0,64 under calm conditions for 5-minute gaps to 0,07 under those of storm for hourly intervals. The applicability limits of the method are determined, enabling development of recommendations for the practical use of reconstructed data