In this situation, a family goodbye gift would be wonderful.
I was a nanny for years and never received severance. Then again, I was never asked to leave a job, but some jobs, like yours, just sort of 'died out'. The kids got older and I usually needed more hours, so it was a mutual parting of ways.
Do offer a way to stay in touch. One family I was a nanny for-- we are still close. I communicate with the girls independently when they are out of town (they are 18 and 23 now)-- one just sent me a card the other day. I also still go for walks and tea with their mom, who has become a good friend. Her family held my son the day he was born, just as I did when their youngest was brought into the world. Enjoy the connection and a well-chosen gift will be appreciated!