Frequency-based analysis techniques such as response spectrum analysis (RSA) are widely used for designing bridges in seismically active regions. Two well-known analysis procedures that underlie RSA are the solution of the eigenproblem and the approximation of the solution to the eigenproblem (i.e., approximation of eigenvectors and eigenvalues) through use of force-dependent Ritz vectors. While frequency-based methods have achieved widespread adoption in practice, certain simplifications remain common, such as neglecting soil-structure interaction (SSI) due to a fixed-base assumption. In the present study, frequency-based techniques packaged within a research version of a design-oriented computational tool are employed to analyze, assess, and compare results obtained from RSA with use of the eigenanalysis, and separately, Ritz vector approaches. Importantly, for the bridge configurations analyzed, SSI is taken into account. As outcomes, the potential benefits of the Ritz vector approach (as well as modeling strategies) are demonstrated. The study outcomes are intended to aid practicing engineers when the need to account for SSI is recognized as pertinent to a given bridge seismic design application.