In the pursuit of real-time motion planning, a commonly adopted practice is\nto compute a trajectory by running a planning algorithm on a simplified,\nlow-dimensional dynamical model, and then employ a feedback tracking controller\nthat tracks such a trajectory by accounting for the full, high-dimensional\nsystem dynamics. While this strategy of planning with model mismatch generally\nyields fast computation times, there are no guarantees of dynamic feasibility,\nwhich hampers application to safety-critical systems. Building upon recent work\nthat addressed this problem through the lens of Hamilton-Jacobi (HJ)\nreachability, we devise an algorithmic framework whereby one computes, offline,\nfor a pair of "planner" (i.e., low-dimensional) and "tracking" (i.e.,\nhigh-dimensional) models, a feedback tracking controller and associated\ntracking bound. This bound is then used as a safety margin when generating\nmotion plans via the low-dimensional model. Specifically, we harness the\ncomputational tool of sum-of-squares (SOS) programming to design a bilinear\noptimization algorithm for the computation of the feedback tracking controller\nand associated tracking bound. The algorithm is demonstrated via numerical\nexperiments, with an emphasis on investigating the trade-off between the\nincreased computational scalability afforded by SOS and its intrinsic\nconservativeness. Collectively, our results enable scaling the appealing\nstrategy of planning with model mismatch to systems that are beyond the reach\nof HJ analysis, while maintaining safety guarantees.\n