Constructing a reduced-order controller from a high-dimensional plant is commonly necessary. The "reduce-then-design" approach constructs the controller from a reduced-order plant; "design-then-reduce" reduces a full-order controller. In both cases, we present sufficient conditions for the full-order plant and reduced-order controller to achieve closed-loop stability or performance. These conditions, motivated primarily by the nu-gap metric, reveal model reduction orders that guarantee stability or performance. The control of the linearized Ginzburg-Landau system provides validation.