An energy recovery LINAC (ERL) is being constructed at Brookhaven National Laboratory that will involve a superconducting LINAC along with a superconducting electron gun, all operating at 703.75 MHz. The ERL will serve as a testbed for the concepts and technologies required to implement future upgrades in the Relativistic Heavy Ion Collider (RHIC). Because of the high current and high charge requirements of the ERL, effective higher-order mode (HOM) damping is an essential component of the ERL research and development program. This thesis focuses on three areas of HOM characterization and damping development: damping of HOMs in the five-cell LINAC, use of the electron gun fundamental power couplers (FPCs) to damp HOMs, and the development of a ceramic/ferrite damper for the electron gun. The five-cell LINAC uses an HOM load lined with ferrite and attached to the beam-pipe on either side of the cavity. These studies characterized the frequency-dependent nature of the ferrite absorbing material and derived a set of "portable" ferrite parameters that simplified simulation work. Using these "portable" parameters, it was determined that the ferrite absorber is effective in damping the HOMs of the five-cell cavity over a range of frequencies. In addition, higher-order mode damping in the electron gun was studied using the fundamental power couplers. The gun cavity is a superconducting half-cell structure designed to accelerate electrons to an energy of 2.5 MeV and features dual fundamental power couplers. The HOMs of the gun cavity were studied along with the damping capabilities of the FPCs. Simulation studies determined that the FPCs couple strongly to many of the HOMs studied. However, the transition between the coaxial FPCs and the waveguide that feeds power to the FPCs is a "doorknob" type transition, and it was found that this component shows the best transmission qualities between 1 and 2 GHz, thus limiting the damping capabilities of the FPCs to this bandwidth. It remains to be seen how the FPCs will perform under actual conditions. Finally, the development of a ceramic/ferrite damper was described for the electron gun. The damper features a lossless alumina ceramic break surrounded by a ferrite load and was designed to isolate the vacuum chamber from the ferrite tiles. Various studies were conducted using simulation and prototype designs, and it was determined that the ceramic/ferrite load can be effective in damping higher-order modes of the gun cavity. Analytical calculations along with simulation show that the ceramic tends to alter the field distribution of higher-order modes and change the damping qualities depending on the frequency. The effectiveness of the damping for a given mode depends on a variety of factors including the thickness of the ceramic, the spacing between the ceramic and ferrite layers, and the diameter of the inner ceramic surface.