I found cape as promontoro, cloak as mantelo and coat as vesto.
Promontoro translates also as "Promontory," a high rock or hill over a level area (as in an ocean) which translation of "cape" would be geographic, not a vestment. Near as I can figure, Superman's cape would be mantelo or pelerino, but certainly wouldn't be promontoro or kabo no matter how strong he is.
Kudos on acquiring an English-Esperanto dictionary. Can you add notes to it?
Not that I know of, I also have this Esperanto-English dictionary, but it doesn't have as much. http://esperanto-panorama.net/vortaro/eoen.htm and this one is defining the Esperanto words in Esperanto: http://reta-vortaro.de/revo/ but if you scroll down, it does have translations to various languages and has first meaning for "mantelo" as cape, cloak, mantle and second meaning as coat. I think from now on I will check the last one first.
I like to have a decent paper dictionary just for the opportunity to scribble comments, notes, etc. in the margins. I've been told one can do that with a kindle, but I haven't figured out how, yet. There are also a couple of Eo Dictionary apps for Apples & Androids that are fairly affordable. One of them just gives a one or two word definition, then, if the word is picked, will take you to the appropriate Wiktionary (this includes language) page.