In this thesis, I examine filtering based stabilization methods to design new regularized reduced order models (ROMs) for under-resolved simulations of unsteady, nonlinear, convection-dominated systems. The new ROMs proposed are variable delta filtering applied to the evolve-filter-relax ROM (V-EFR ROM), variable delta filtering applied to the Leray ROM, and approximate deconvolution Leray ROM (ADL-ROM). They are tested in the numerical setting of Burgers equation, a nonlinear, time dependent problem with one spatial dimension. Regularization is considered for the low viscosity, convection dominated setting. / Master of Science / Numerical solutions of partial differential equations may not be able to be efficiently computed in a way that fully captures the true behavior of the underlying model or differential equation, especially if significant changes in the solution to the differential equation occur over a very small spatial area. In this case, non-physical numerical artifacts may appear in the computed solution. We discuss methods of treating these calculations with a goal of improving the fidelity of numerical solutions with respect to the original model.