I have the maxed out 2011 13" MacBook Air. When I go into system preferences, I don't see an option to enable handoff on this device.
What can I do to make it work, because my machine is supposed to support continuity?
AFAIK there's no official breakdown of what's required for continuity and which machines are 'supposed' to support it. People seem to think Bluetooth 4.0/LE is the only requirement but I don't think it is.
As an MBA 2011 13" owner I can tell you that handoff doesn't work for me, nor for anyone I've come across with the same model.
The option was removed from System Preferences a few betas back. Interestingly if you type 'Handoff' in the Sys Pref search box it will try to take you to the General section but of course it's not actually there.
Airdrop with iPhones also doesn't work on MBA 2011.
Other features of continuity like SMS relay and iPhone calls do work though.
There's still a chance Handoff and Airdrop will be enabled for the final release.