There are a few consumer-facing easy-to-obtain devices that you could use for this, although they don't quite transmit in real-time (they'll transmit updates down to every 2 minutes). Spot and inReach are aimed at more casual users, and Spidertracks offers real-time tracking that might be considered targeting more of the commercial or "prosumer" market, but they still transmit updates every 1-2 minutes.
They all work in a similar fashion: rather than some kind of ground-based radar, they utilize a combination of GPS to calculate your location and use the Iridium Satellite communications network to transmit it (so it doesn't rely on cellular signals and has global coverage), they transmit on an interval you decide to a website that your interested party could monitor. This is the key difference from other answers that use an app on a device: even if the app is linked to a real-time tracking service like Map my Tracks, your phone or tablet will still be relying on the cellular network (which you're technically not supposed to be using in flight), and even if it does work, it could be intermittent. These devices link into the Iridium Satellite network for global coverage.
The three devices are: Spot Satellite Communicator and the DeLorme (now owned by Garmin) inReach, and Spidertracks.
This isn't a free service, there is a monthly fee for using the devices.
Spot is around USD$150
inReach is around USD$350
Spidertracks start at USD$1000
In July 2016 ($USD)
inReach: Allows tracking updates every 10+ minutes ($15/month) or the 99/month package allows for updates every 2+ minutes.
Spot: 50/year allows 5, 10, 15... minute tracking update intervals or $150/year: 2.5+ minute tracking updates.
Spidertracks has various plans, basically you pay by reporting point the range is $0.05 - $0.13 per reporting point.
DeLorme inReach:
Spot Satellite Personal Tracker:
Spidertracks
Example of the web interface from Spidertracks for real-time tracking
