I have a stand-alone HRM, a Cat Eye, because I use it in other athletic pursuits (heresy!).
I use it so I know how close I am to my max HR -- then I have an idea how long I can stay there -- as well as to focus on staying at 75-80% of my max HR during tempo training. Perceived exertion has its place, to be sure. There will be times when I perceive that I'm this () close to dying when in reality I'm at 80% and need a day off.
As someone else said, it helps to keep me focused, esp. on the back of the tandem, where opportunities to gawk & talk abound.