Tools based on the bifurcation and continuation method have been found to be extremely useful for studying multiparameter nonlinear dynamical systems under state and parameter-constrained conditions. Because of inherent limitations of the existing methodologies, however, application of continuation techniques to certain types of problems has remained cumbersome and even computationally challenging. This paper provides an alternate direct approach in MATLAB® using its continuation subroutine MATCONT to extend the capabilities of continuation techniques in an attempt to accommodate a wide variety of constrained dynamics problems. Published results in the literature are first reproduced for validation of the proposed approach. A control problem of scheduling gains for the longitudinal flight dynamics of an aircraft is next presented to show usefulness of the proposed methodology, followed by solutions to an aircraft conceptual design problem involving wing morphing with eigenvalue constraints, with the difficulties of the selected problems increasing in that order.