I heat with heat pumps instead of natural gas.
(BTW: Not sure if you did the numbers, but with my solar system, electricity is so darn cheap that running a heat pump (air) is cheaper than running a natural gas furnace. If my house was smaller.)
I also put in a wood stove and light the fire when it's extremely cold and I'm home for awhile. Wood is carbon neutral. (The carbon released is carbon that the tree captured while it was alive.) (Although some people like to point out that burning wood releases particulates and other nasty pollutants.)