Whats the best way to transport a music collection to another hard drive without missing files?

Whats the best way to transport a music collection to another hard drive without missing files?  I've moved computers before and have had missing files in the past.  I'd love to avoid that problem if possible.  I've warped most of my collection in Ableton, and would like to keep the files warped without having to do it again.  Thanks for your help!