I was under the impression that my mid-2011 MacBook Air would support the technology but it wasn't until I tried to get it to work that the penny dropped, and although the hardware supports Handoff and Continuity, my MBA was telling me a different story - until now.
When I did a comparison of the Bluetooth configuration on the MBA and my late 2012 iMac (which categorically does support Handoff out of the box) it seemed that the specs were actually better on the older machine. Which seemed a bit perverse. So I did some more investigation and discovered that the ability of any particular model of Mac to handle Handoff depends on hardware, software and a configuration (.kext) file which contains the model names of supported machines. If the appropriate .kext files are modified, it is possible to persuade the OS that the machine will support Continuity and Handoff.
After a bit more research I found this web site from which you can download a tool which will patch the appropriate files and enable you to turn on Handoff. The whole process took less than 10 minutes and my first test proved successful. I loaded my web mail page in Safari and switched on my iPhone and in the bottom left corner of the lock screen was the Safari icon. I swiped up on the icon and my web mail page appeared on my iPhone.
As with any system modification you do this at your own risk, and you absolutely must read the instructions before you attempt to make the modification, and it would be prudent to take a back-up or better clone your start-up disk before running the tool.
If this works for you, don't forget to make a donation to the guys who did all the work. There's a place for you to do so on the site!