Dielectric properties of CaNdAlO4monocrystals, a prospective substrate material for the deposition of high‐Tcsuperconductors, were measured with high accuracy at microwave frequencies from 8 to 40 GHz in the temperature range from 10 to 300 K by measuring the resonant frequencies of a completely filled resonant cavity. The material was found to be highly anisotropic. At 300 K it exhibits the dielectric constant alongcaxis &egr;’c= 17.68, while the dielectric constant in thea‐bplane is &egr;’=19.62, and loss tangent tan &dgr;c&bartil; tan &dgr; &bartil; 5.1× 10−4. Both &egr;’cand &egr;’depend strongly on temperature and their thermal coefficients have opposite signs, apparently a unique property of CaNdAlO4. Below 160 K microwave losses caused by electric field perpendicular to the opticalcaxis increase with decreasing temperature, exhibiting a maximum near 65 K followed by a minimum at 30 K. It is suggested that neodymium ions in CaNdAlO4at lower temperatures become magnetically ordered, causing an increase of magnetic permeability &mgr;’c≳ 1 and a significant increase of magnetic losses at microwave frequencies. A crystallographic phase transition below 60 K cannot also be excluded.