Precise knowledge of the absolute value and frequency dependence of the dielectric permittivity of ice is the basis for interpretation of radio echo sounding data on glaciers and ice sheets. However, in the range of radio-frequencies, data from direct measurements of the permittivity are sparse, and partially lacking uncertainty estimates. Here, we present new results for artificial and natural ice samples obtained by means of frequency-dependent measurements from 10 MHz to 1.5 GHz with a coaxial transmission line cell. Measurements on eight artificial ice samples grown from ultra-pure water within the cell yield a mean value for the real part of the relative permittivity of 3.18 ± 0.01 at − 20 °C. Sole evidence for dispersion is detected for frequencies below 10 MHz, possibly attributed to the Debye-type relaxation behavior. Investigation of the crystal orientation of the artificial ice samples reveals the c-axes to be predominantly parallel to the electric field inside the cell and allows to calculate a value representative for isotropic crystal orientation of 3.16 ± 0.01. Measurements on acid-doped artificial ice show a linear dependence of the real part with acidity with a gradient of (21.1 ± 3.9) [1/M]. The real part of the relative permittivity of natural firn and ice samples from a high Alpine glacier range from 2.02 at a density of 0.515 g/cm3 to 3.08 at 0.875 g/cm3. Quasi-continuous measurements with the present setup on an alpine firn core are now possible, with resolution depending on the coaxial cell's length, for direct comparison with the established dielectric profiling method.