I make prototypes of stuff like this as a hobby. You could use a fairly inexpensive SoC that has Wifi/Bluetooth built in ($6), attach a module for 4G connection (~$50), and give it a huge battery so that it can lasts a few weeks. It would be asleep most of the time, and wake up every 2 minutes or so to check for updates. Meaning you'd have to stand there at the door for a couple minutes before it'd give you access.
Thanks for the info regarding the components.
I wonder if there'd actually be a market for this kind of thing.. i.e. One person unlocking access to physical keys in a lockbox at a remote location so that another person can gain access to something. It would be used in a temporary installation, not like ring.com installed at a front door of a house or remote access tech built into cars these days.
Another case of technology in search of a problem... :-(
I mean something like Ring (1) plus MasterLock 5400D (2) plus embedded 4G mobile connectivity. It must not be a permanent installation (like Ring) and it should not require visitors to be pre-registered (like Supra Keys (3)) in order to access the property (for example contractors, repair staff, delivery personnel, etc)
If something like this already exists, please let me know.
(1) http://www.ring.com (2) http://www.masterlock.com/personal-use/product/5400D (3) http://www.supraekey.com/Products/Pages/Products.aspx
* edits: fixed typos