Both geophysical fluid-dynamical (GFD) systems and magnetohydrodynamical (MHD) systems are governed by symmetries that manifest as conservation laws, such as those for energy, momentum, and circulation. Preserving these conservation laws in numerical simulations improves long-time stability and physical fidelity. Simultaneously, fully resolving the wide range of scales motion in these dynamical systems is computationally prohibitive, necessitating complexity reduction that fulfils the constraints imposed by the conservation laws. We will highlight the applicability of circulation-preserving noise (stochastic advection by Lie transport, SALT) and energy-preserving noise (stochastic forcing by Lie transport, SFLT) as structure- preserving approaches for reduced-complexity modelling of GFD and MHD systems. These methods introduce carefully designed stochastic terms to account for the influence of unresolved dynamics while maintaining key physical invariants. SALT and SFLT have previously been studied in the context of uncertainty quantification and data assimilation for two-dimensional turbulence, employing a low-rank stochastic forcing calibrated from observational data. More recently, SALT and SFLT formulations have been derived for rotating shallow water magnetohydrodynamics (RSW-MHD), enabling reduced-complexity stochastic models for problems relevant to space weather and solar physics. We will discuss ongoing work on on the calibration of stochastic forcing for reduced-order RSW-MHD test cases using high-fidelity data.