The shielding effectiveness of a 'pigtail' connection between a coaxial transmission line and a ground plane is treated rigorously by the method of moments, as a function of the type and number of pigtails and frequency. Numerical results show that the type of pigtail connection is crucial with regard to radiation and shielding effectiveness, even though the pigtail itself does not radiate significantly. All pigtails are not equal, even though they can be short electrically. A short pigtail is significantly better than a longer one. A long pigtail connection can actually enhance radiation. Finally, multiple pigtails yield significant improvement over the single pigtail only for short pigtails. Numerical and experimental results are compared and found to be in good agreement. >