Electromagnetic scattering problems involving uncertain or deformable geometries give rise to families of boundary integral operators whose domains, kernels, and trace spaces vary with the scatterer. Understanding and exploiting this geometric dependence is essential for efficient multi-query simulations, uncertainty quantification, and inverse problems. In this talk, I will discuss the holomorphic dependence of Maxwell boundary integral operators on geometric deformations, using suitable transformations to a fixed reference surface. Particular attention will be given to electromagnetic trace spaces, surface differential operators, and Calderón identities. Building on this structure, I will discuss computational strategies for reusing operator-based preconditioners across families of geometries, including recent developments in frozen Calderón preconditioning. The talk connects the functional analysis of geometry-dependent boundary integral operators with efficient numerical methods for electromagnetic scattering under shape variations.