  We study generalised quantum waveguides in the presence of moderate and
strong external magnetic fields. Applying recent results on the adiabatic limit
of the connection Laplacian we show how to construct and compute effective
Hamiltonians that allow, in particular, for a detailed spectral analysis of
magnetic waveguide Hamiltonians. We apply our general construction to a number
of explicit examples, most of which are not covered by previous results.
