I've done canning of jams and jellies. I would like to make caramel and butterscotch syrups and jar them to give away, too, but I'm not sure if this is do-able since they contain butter and cream. Can this be done safely at home? If so, how long would they be good for?
I haven't seen a butterscotch canned recipe but the ball blue book has a couple syrup canning recipes that look fantastic. If you do any canning you should have this book. The recipes are invaluable.
These recipes use the hot water bath technique. The extremely high sugar content would be enough to keep it preserved. Modifying one to be butterscotch should be straight forward.
I wouldn't try any experiments that reduce the sugar content because then we're getting into the risk-of-horrible-paralyzing-death area of canning.
Different types of caramel can be stored for different amounts of time. Caramel syrup is stored well in an air-tight glass container for a few months in a fridge. If you make caramel sweets they are best stored if wrapped in wax paper to prevent sticking and then put inside a freezer bag. You can freeze them for a few months (if you can resist them that long!)