The inverse braid monoid script J SignBn consists of n-string braids from which some subset of the strings has been deleted. Such partial braids may be composed by concatenation followed by the deletion of any incomplete strings, and this operation gives script J SignBn the structure of an inverse monoid. We derive presentations of script J SignB n by first using a groupoid presentation, and then deriving equivalent inverse monoid presentations. In particular, we offer a new derivation of the presentation for script J SignBn that has been given by Easdown and Lavers. © World Scientific Publishing Company.