I also use Cyclemeter, and I generally like it. I suggested to them that they tie into the iPhone's accelerometer to detect sudden deceleration and send alerts. They passed on that idea. I have used it to send periodic updates to my wife when I was riding the Southern Tier, which she told me reduced (but did not eliminate) her worries about me. Apple treats Messages (its texting app) as a crown jewel, which is why Cyclemeter can't tie into it. In theory, one could route an e-mail message through a service like Zapier to trigger a text message. One can also post regular updates to Twitter or Facebook, although I don't consider that an improvement.
One thing you can do with an iPhone, without using any 3rd-party apps, is open the Health app and set a Medical ID profile, which will include contact numbers and more information than you could fit on an ID bracelet. This info can be called up by anyone with access to your phone (even when the phone is locked) if they know to look for it. I've never asked a first responder if they're aware of this feature--I hope they are. I assume something similar is available on Android phones.