Is there a device that will keep me from losing my Android phone? Recently I lost my phone and have had to order a replacement. It seems that there should be some sort of device I could use that would sound an alarm when I separate more than, say three meters from my phone. Does anyone know of such a device?

I tried searching for a proximity sensor but got only irrelevant stuff about the sensor that detects when the phone is being held up to the ear. It seems that "proximity sensor" is the wrong search term.
There's no easy way to control the mentioned scenario, since you may get away from your phone, leaving behind the device used to alert you.
I've been playing around with an APP, that basically runs a task when a certain action occurs within your phone.
The test I performed, was having my phone playing a really loud sound if my phone gets disconnected from the bluetooth earpiece. It works, I go away from my phone and as soon as the bluetooth gets out of range, the phone starts to play the music. I hear the music and remind myself that my phone was left behind.
Of course that if you use Dragon V2 Bluetooth Headset, it will only get out of range after 100 meters, which is roughly 10 times more distance than a regular Bluetooth earpiece. :)

Tasker
Tasker by Crafty Apps available from Google Play Store (4,49€)
From their website you have a free 14-day trial download.