  We study the recently introduced 'critically coupled' model of magnetic
Skyrmions, generalising it to thin films with curved geometry. The model feels
keenly the extrinsic geometry of the film in three-dimensional space. We find
exact Skyrmion solutions on spherical, conical and cylindrical thin films.
Axially symmetric solutions on cylindrical films are described by kinks
tunnelling between 'vacua'. For the model defined on general compact thin
films, we prove the existence of energy minimising multi-Skyrmion solutions and
construct the (resolved) moduli space of these solutions.
