The emergence of the internet saw lots of people swapping pens and paper for keyboards, which brought the problem to the fore. These early denizens of cyberspace could've used the h-metodo but because of its potential problems chose another approach; they used the letter X as the trigger, placing it after each of the letters which required the accent:
cx = ĉ, gx = ĝ, hx = ĥ, jx = ĵ, sx = ŝ, ux = ŭ
By using a letter which wasn't part of Esperanto's own alphabet as the trigger, they removed the ambiguity which sometimes resulted from the h-metodo. The x-metodo isn't officially recognised but it is by a long shot much more common than the earlier alternative. Many Esperanto sites, including this one, assume its users will use the x-metodo and automatically change the letter to the accented version.