This note discusses numerical computation of guiding center orbits in tokamaks using cylindrical coordinates and several magnetic coordinates. Some subtle things involved in using a particular kind of magnetic coordinates called field-line-following coordinates are discussed (I am using this kind of coordinates in developing a new module in GEM code). We assume a general tokamak magnetic field specified numerically (provided by the EFIT G-file). This note is evolving, beginning with my first try of computing guiding-center motion in Solovev analytical equilibrium using cylindrical coordinates, and then extending to general numerical magnetic field, and later using magnetic coordinates.