Panel methods are frequently applied to aerodynamic shape optimization problems due to their fast turnaround time and ability to model arbitrary geometries. Despite being advantageous for design optimization, we have found that panel methods can predict nonphysical results for unconventional geometries. This paper presents robust methods to solve optimization problems using panel methods that are not susceptible to numerical errors. Important factors are highlighted with regard to choice in boundary conditions, induced drag calculation, wake modeling, and regularization. Two parameterization methods are introduced where wing geometry is defined locally by airfoils at discrete spanwise positions and regularized by filtering along the span. Such methods of defining the geometry locally enlarge the design space and allow the optimizer to converge to reliable designs. Results also suggest the following: 1) enforcing a Dirichlet boundary condition rather than a Neumann formulation provides significant cost savings in gradient calculations, 2) far-field force calculations should be adopted for optimization problems as numerical errors in surface pressure integration have a strong influence on the gradients, and 3) the additional design freedom of a B-spline parameterization can be disadvantageous as the low fidelity of the inviscid model cannot correctly capture aerodynamic properties of irregular airfoil geometries.