Personally, I don't honour deities, but I
do make offerings - my offerings are made to the elements, and to the creatures that inhabit them. I'll try and explain but there's every chance it won't make sense
Since I don't worship and have no ties to any particular pantheon or deity, I don't make offerings to any of them. I have nothing at all against eclectic worship or chaos magic, but it just doesn't feel right to me to make an offering to a God or Goddess and then happily ignore their existence until the next time I need them. However, I do believe in the power of the elements (earth, air, water, fire, spirit), and I will make offerings to them and ask them to guide me if needs be. Within that, I will accept any personification of that element - whether its a salamander or an angel with a flaming sword for fire, a mermaid or a mussel for water. So, my offerings are made to the element and any spirit or creature with a link to that element is particularly welcome to partake of it.
I try to make my offerings practical as well. If I make an offering to earth, I'll plant something, ensure that a struggling plant is well nourished, put out food for animals in the winter and hatching/birthing seasons and pick up litter and debris. For water, I make sure the ponds are welcoming to waterlife in all forms, clear the duckweed and dead lily pads from them, fish the carrier bags out of the local stream, feed fish, frogs or wading birds and possibly make a little libation to the water. To fire I offer fuel - building a good fire is an offering in itself, feeding it good seasoned logs and making sure it is properly fed with air, or if its not possible to make a true fire, I light a candle, making sure not to extinguish it with my breath once my offering is made. For air I make sure that the birds who visit my garden are protected, that they are fed and welcomed. I offer incense or burn oils, or make wind chimes or mobiles to hang in the breeze. And for spirit, my offerings are usually made whilst pathworking or meditating - whatever (within reason) is asked of me or needs doing.
In between these, my offerings are usually made in thanks for something I've been given. For instance, I spent this morning listening to the blackbirds and robins singing beautifully outside my office window, so half of my mid-morning flapjack is now on the grass outside the window for them - simple but effective