You can spray as close as you can, but don't get any Glyphosate on the leaves. Avoid mist setting where the product might drift onto the leaves.
Mike

Yippee! Thank you, Mike

Except that azaleas are liable to have lots of roots quite high up in any organic litter layer that may be present on top of the soil.

C. Whitcomb (Establishment and Maintenance of Landscape Plants, revised 1991 edition) reports episodes where it really appeared there must have been root absorption of glyphosate. Trees were actually killed. On the other hand, L. Chalker-Scott (see her web site) says it doesn't happen.

Here is the link to this particular L. Chalker-Scott posting.

Here general website is:

http://www.puyallup.wsu.edu/~linda%20chalker-scott/horticultural%20myths_files/index.html

Here is a link that might be useful: The Myth of Wandering Weedkiller

I thought I was being careful, but lost a couple of young [2nd year] azaleas.

When I use glyphosate around rhododendrons and azaleas, there are a number of precautions I take:

1) use a very low pressure so the spray is a spray and not a mist.
2) only use glyphosate when there is no wind or very little wind.
3) have a barrier, like a piece of cardboard, to put between weeds and good plants. Plainly mark which is the contaminated side of the card.
4) wipe off any spray that gets on a good plant or, better yet, remove the leaf that was hit.

Using these precautions, I have never had any problems.

A nurseryman here couldn't get rhododendron cuttings to root well after using glyphosate around the stock plants. You really want to be careful with herbicides, treated areas can look okay while non-target plants are actually being affected.