  The exact analytical solutions for vacuum electromagnetic fields of slowly
rotating magnetized compact stars in conformal gravity have been studied.
Taking the realistic dipolar magnetic field configuration for the star,
analytical solutions of the Maxwell equations for the near zone magnetic and
the electric fields exterior to a slowly rotating magnetized relativistic star
in conformal gravity are obtained. In addition, the dipolar electromagnetic
radiation and energy losses from the rotating magnetized compact star in
conformal gravity have been studied. With the aim to find observational
constraints on the $L$ parameter of conformal gravity, the theoretical results
for the electromagnetic radiation from the rotating magnetized relativistic
star in conformal gravity have been combined with the precise observational
data on the radio pulsars periods slow down and it is estimated that the upper
limit i.e. the maximum value of the parameter of conformal gravity is less than
$L \lesssim 9.5 \times 10^5\textrm{cm}$ ($L/M \lesssim 5$).
