Morale is a feeling and the best way to track it is by constantly talking to your team. However, your team members won't open their hearts to you unless they trust you, but, if you have some really extrovert team members, they will just tell you that their morale is suffering when it's really bad.
Additionally, and as you said, morale is proportional to productivity, so if morale is low, then so is productivity.
Here are some hints that your team morale is low:
- Low self esteem
- Low productivity
- Most team members coming late to work
- Team members become clock watchers (they keep checking the time for the lunch break or for leaving)
- Team members don't want to work on the project anymore, and they tell you this.
- The once "star of the team" will have a problem tackling even the easiest tasks.
I've seen project managers setup a small form on their Intranet, just for tracking team morale. Every team member visits this form every morning, which has only one question: "How do you feel today?", and the response consists of a multiple choice of smilies (angry, sad, neutral, happy, ecstatic). Project managers then will be able to see reports based on the information filled in. For example, if for the whole week, most team members are below neutral, then you have some serious issues on your project that you need to take care of. I think this is a good way to track team morale, although it looks a bit odd and maybe stupid.