Oxygen consumption is the best way to assess calorie burn, but this is hard to measure. Generally (but not always), your heart rate increases in a predictable fashion as it works harder to pump the oxygen from your lungs to the muscles that need it.
If you are doing cardio at a steady pace, www.shapesense.com/fitness-exercise/calcul
will allow you to estimate calories burned from your heart rate.
If you are mixing the pace up a bit, an HRM is probably the only way to assess this.
However, people with high blood pressure, or taking certain medications, will see their HR increase much faster than the exercise truly warrants, and the heart rate method will not produce accurate results.