Sleep

Sleep to the nearest minute or hour

This can be done with some bash arithmetic and applying modulus to 60 seconds for 1 minute or 3600 seconds for 1 hour.

# Next minute
sleep $((60 - `date +%s` % 60))

# Next hour
sleep $((3600 - `date +%s` % 3600))

With millisecond precision

If you need to synchronize a task by the millisecond, you can use date +%s%N which will print the timestamp with nanoseconds. Divide by 1000 for milliseconds and apply the same logic as above.