Not all pollinator gardens need to be a flower bed located in full sun. In fact, pollinators need a wide variety of plants that grow in different conditions. Butterflies and moths in particular need “host plants” that provide food for their caterpillar stage of development. In other words, without those host plants, there will be no butterflies and moths.
For example, many common native trees like oaks, cherries, hackberries and elms are host plants for a wide variety of butterflies and moths. Some butterfly caterpillars like the Gulf Fritillary will only feed on Passionflower vine. These specific relationships between native insects and native plants is why it is crucial to have not only flowers for nectar and pollen but trees, shrubs, grasses and vines to provide food for caterpillars and other insect larvae. You can see the specific relationship between native plants and butterflies in this list: Native Plants that Support Butterflies (and other pollinators) A worldwide database of host plants for butterfly and moths can be found here: https://www.nhm.ac.uk/our-science/data/hostplants/search/index.dsml
The list below provides a sampling of small native trees, shrubs, vines, grasses and perennials by growing conditions. Even if you only have a shady location, you can support pollinators in your landscape!