Bird's nest Anthurium plants are known for producing open-pollinated berries; their inflorescences last so long that when one is shedding pollen, a newer one is receptive to that pollen. That's how you got berry set on yours. The seeds are inside the berries, usually one per berry. You need to squish the berries individually on paper towels so as to reveal the seed. Then rub the seed gently on the dry paper towel so as to remove as much as the mucous coating as possible, then soak in distilled water overnight before planting on moist planting mix. I use a covered container, like a mini greenhouse. Often the clear plastic containers you get with some take-out food are ideal for this so long as they have (or you make) holes in the bottom for drainage.

The seeds germinate after a week or so and you will have plenty of Anthuriums.

LariAnn Garner
Aroidia Research

Here is a link that might be useful: Cleaning Anthurium and Philo seeds

Many thanks LariAnn, I'll give it a shot.