You can easily grow marigolds next season from the harvested seeds. This is a guide about harvesting marigold seeds.
How can I gather the seeds from my mom's marigolds and mums so that we can grow more next year?
By Slingshot_317 from TX
Pinch the dried up blossom from it's stem near the bottom of seed pod and store in paper bag until ready to sow. When you are ready to plant the seeds, gently rub the dried pod and all the seeds will freely fall open. If you have several colors of marigolds you may want to separate the colors by labeling each bag.
You can grow mums from cuttings taken from plant by the 4th of July. Just put cuttings in ground and keep them watered.
On marigolds, the seeds are hooked to the bottom of the petals. Pull them out when the flower has wilted and dried out. I don't know about mums, sorry.
Some varieties are hybrids and although they produce seeds, they won't grow.