Abstract - In reduced basis methods for partial differential equations, computationally expensive numerical solutions are replaced by cheaper "low-fidelity" approximations. Rigorous error estimates are very important to ensure that computational savings are not obtained at the cost of unacceptable loss of accuracy. Typically, these estimates are measured with respect to the high-fidelity numerical solution, rather than the exact solution to the PDE. In this talk, a reduced basis method utilizing a least-squares finite element discretization is presented. The least-squares discretization allows for the development of error bounds between the low-fidelity solution and the exact solution.