If you want a turn-key solution, you probably want to look for mPERS devices, and find a monitoring company with a decent subscription plan. Many will subsidize the cellular part by reselling that service and rolling it all into one plan, but you'll pay ~$30-$50/mo.
If your needs are more sporadic (family outings, etc.), you can find some systems that let you get updates via text messages (you send a message to the device, and it responds with location and/or you can put it in a mode where it auto-updates at some interval). Then all you need is the cellular plan (I found h2o wireless to be the most cost-effective pay-as-you-go plan here). You can also assign a geo fence to the device based on its current location, and some allow you to also get alerts if the device exceeds a speed limit (such as in a child being abducted and taken away in a car/etc.)
An issue with the DIYish approach is that you have lag time for sending/receiving text messages at times, and if you have an actual emergency, juggling your phone to send/receive texts and calling police/etc. could be a bit cumbersome/stressful.
As you mention, getting the kids to wear the device could be an issue, and if you are worried about abduction-type events, the devices are going to be fairly obvious (and thus likely removed).