I missed a connection from AMS to SVG on my last trip due to weather related delay from origin of LBA in the UK on a non-refun/non-reroute/non-rebook E fare.

Head straight to the transfer desk. My partner and I were re-booked onto the next available flight and upgraded to Europe Select! Woot! 6hrs doesn't seem so bad when it is clouded in bubbles.... (edit: and that is with an ivory/petroleum club card)

Under the new EU legislation, an airline is obliged to rebook free of charge if you miss a flight due to "circumstances that could not reasonably have been forseen" and they are obliged to look after you if you are stranded including but not limited to overnight accomodation. This is, of course, if your outward and onward journey are with the same carrier or codeshare and you are originating, transiting or destined for an airport in the EU.

This legislation though has not been tested in court - so good luck with an appeal