Elaphebolion and is, like all third days after the Noumenia, sacred to Athena. Special libations were poured to her on this day, along with extra sacrifices. I like lighting a bit of frankincense and saying Homeric Hymn 39 to Athena, my favorite of Her hymns. Sometimes I enjoy writing a new hymn for Her, or offering a piece of sculpture or fiber-art that I've worked on to Her. Anything I can do to mark this day as special above and beyond my daily devotions to Athena I see as a good thing to do on this day.
How do you honor your patron Gods? When do you honor them?