Most electromagnetic problems can be reduced to either integrating oscillatory integrals or summing up complex series. However, limits of the integrals and the series usually extend to infinity, and, in addition, they may be slowly convergent. Therefore numerically efficient techniques for evaluating the integrals or for calculating the sum of an infinite series have to be used to make the numerical solution feasible and attractive. In the literature there are a wide range of applications of such methods to various EM problems. In this paper our main aim is to critically examine the popular series transformation (acceleration) methods which are used in electromagnetic problems and to introduce a new acceleration technique for integrals involving Bessel functions and sinusoidal functions.