A technique is described for achieving high accuracy (relative error up to ≈0.001%) for measuring the absolute wavelengths of the spectral lines of multiply charged ions with an average (Z = 17–25) by the nuclear charge, the spectra of which can be used for plasma diagnostics in laboratory astrophysics experiments. It is based on irradiation with subnanosecond laser pulses with an intensity of 1015–1016 W/cm2 targets with a multicomponent chemical composition, including atoms with both medium and low Z. The presence of the latter ensures the presence in the emission spectrum of the resulting laser plasma of lines of hydrogen-like ions used as references. An atomic-kinetic code was created, and the intensities of possible reference and investigated spectral lines were calculated. The principles of selecting the target material, the features of the implementation of the technique on the example of a focusing spectrometer with spatial resolution based on spherically curved mica and α-quartz crystals are considered, and specific parameters of spectrometer circuits and types of targets for precision measurement of the wavelengths of spectral lines of helium- and lithium-like ions with nuclear charges Z = 13–25 are given. The results obtained in this work will be used in the planning of fundamental X-ray spectral studies at the ELF laser facility being developed at MEPhI.