ObjectSpace.memsize_of does work in 1.9.3, documented or not:
puts RUBY_VERSION #=>1.9.3
require 'objspace'
p ObjectSpace.memsize_of("a"*23) #=> 23
p ObjectSpace.memsize_of("a"*24) #=> 24
p ObjectSpace.memsize_of("a".*1000) #=> 1000
h = {"a"=>1, "b"=>2}
p ObjectSpace.memsize_of(h) #=> 116