Various error estimation and adaptive refinement techniques for the solution of electromagnetic integral equations were developed. Residual based error estimators and h-refinement implementations were done for the Method of Moments (MoM) solution of electromagnetic integral equations for a number of different problems. Due to high computational cost associated with the MoM, a cheaper solution technique known as the Locally-Corrected Nyström (LCN) method was explored. Several explicit and implicit techniques for error estimation in the LCN solution of electromagnetic integral equations were proposed and implemented for different geometries to successfully identify high-error regions. A simple p-refinement algorithm was developed and implemented for a number of prototype problems using the proposed estimators. Numerical error was found to significantly reduce in the high-error regions after the refinement. A simple computational cost analysis was also presented for the proposed error estimation schemes. Various cost-accuracy trade-offs and problem-specific limitations of different techniques for error estimation were discussed. Finally, a very important problem of slope-mismatch in the global error rates of the solution and the residual was identified. A few methods to compensate for that mismatch using scale factors based on matrix norms were developed.