What about tree cores? No need to cut the trees down and it should work if this Salix species produces annual growth rings. If the trees are small, you could use an increment puncher to get microcores (~2mm diameter). I used that tool on trees with a diameter >3 cm and it worked very well. Basic increment corers are wiedely available from forestry shops.

Increment puncher:

https://brill.com/view/journals/iawa/21/2/article-p169_3.xml?language=en

Willow is a tree that you may not be able to hit the center all the time with an increment borer (as mentioned by Dr. Mohl). Since Salix if cut sprouts back from the roots (coppice), sometimes an increment bore may have two or more stem centers that grew together with time. As I remember, if especially worried about health of tree, return the increment core to the tree, or apply the spray that horticulturalist sand tree surgeons use on cut surfaces. The annual rings can be counted visually, or get a hand lens if the rings are close. Typically, increment cores should not damage or kill tree. If you don’t have any sealant, candle wax would probably due to cover hole, and discourage insects, excess moisture or disease entry.

Thank you dear Mohl. Have you protocol for estimate age of tree with this?

Thanks Dear William. This is a very important point...