Dielectric properties of CaNdAlO4 monocrystals, a prospective substrate material for the deposition of high-T(c) superconductors, 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 along c axis epsilon(c)' = 17.68, while the dielectric constant in the a-b plane is epsilon' = 19.62, and loss tangent tan delta(c) congruent-to tan delta congruent-to 5.1 X 10(-4). Both epsilon(c)' and epsilon' 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 optical c axis increase with decreasing temperature, exhibiting a maximum near 65 K followed by a minimum at 30 K. It is suggested that neodymium ions in CaNdAl04 at lower temperatures become magnetically ordered, causing an increase of magnetic permeability mu(c)' > 1 and a significant increase of magnetic losses at microwave frequencies. A crystallographic phase transition below 60 K cannot also be excluded.