There is no built-in functionality in Redis to supply you with this information.
The available memory is machine-wide. Parsing /proc/meminfo
is indeed a good way to get this info.
See here for a python example: nagios plugins check_memory
We use a similar script on our dedicated redis machines (which run several redis-server instances a piece), that send alerts to our in-house exception handling portal when our memory limit is reached.
Kind regards, TW