  We investigate when a meromorphic connection on a smooth rigid analytic
variety $X$ gives rise to a coadmissible $\mathcal{D}_X$-cap-module, and show
that this is always the case when the roots of the corresponding $b$-functions
are all of positive type. On the other hand, we also give an example of an
integrable connection on the punctured unit disk whose pushforward is not a
coadmissible module.
