Abstract: Recently a Hardy-type inequality for two dimensional waveguides in magnetic fields was established by Tomas Ekholm and Hynek Kovarik. Their theoretical result allows to conclude that eigenvalues will not appear for sufficiently weak curvature of the waveguide, but the proof does not give a good idea about the actual constants involved. We will present numerical examples of this phenomenon, and discuss the size of the constant in the Hardy-type inequality.