Don't know about Cayo district, but BTL has excellent coverage in the cayes off of Placencia.
BTL has coverage for most of the areas behind the reef. If you dont see signal then stand on
deck as high as possible and face the back of the
phone towards the nearest cell tower...these towers are usually near the closest town...at night you can often see their red flashing light for a better fix. Not likely to get coverage down in the Sapodillas. *
Basic cell phones do better than fancy ones. My theory is that the basic phones have more room for the internal
antenna than the fancy ones w all the other stuff crammed inside. My old Nokia dumb
phone out performs smart phones every time...I've joked with guests w fancy phones, which could not get signal, about
renting it to them.