I generally assume the queen to be in the upper 1/3 of the cluster as Grant stated.  I’ve watched swarms alight on branches, and the queen, although not always the first to land, is usually amongst the first arrivers. 

If 
> the queen was in the center of the hanging cluster, it is
> likely that she 
> dropped into the box, 

 if the queen tends to be on or close to the
> trunk of the 
> branch, she is likely left behind, 

I agree with the above, but for a different reason.  

I often position a hive body (or other box,
> basket, net, etc.) 
> under the swarm and sharply jerk a cord that was thrown
> over the branch. 

From my experience, the above is a reason why queens are missed.   

I did a short paper some time ago, titled ‘The Physics of Catching Swarms’.   I found that I had much greater success catching the queen on the first try if the shake method, as typically performed, was not used.   If you could imagine here, when the cord is jerked down, the branch will be propelled through the mass of bees at a rate faster than gravity can cause them to fall, and perhaps the branch will travel into the swarm by a distance of ½  the swarms total length with great force, and this force is then transferred directly to the adhering bees.  

The result is a violent collision and instant displacement of the bees in the upper portion of the cluster causing them to take flight.  Swarm queens are very quick to take flight, and will flee in an instant in reaction to this violent disruption.  An analogy would be 10 beekeepers hanging on tree limb by their finger tips.  To get them beekeepers off that branch, your going to take that tree limb, and slam it down past their elbows and into their heads, and transferring that force directly onto their heads. 

Side shakes were somewhat more effective, less force was transferred to the bees and less flying resulted, along with a higher instance of securing the queen. 

But the shake I found most effective was one that was done not by shake, but by striking the branch in an upwards direction with the palm of the hand, OR direction of the fewest bees adhering.  This resulted in the greatest success rate in capturing the queen.  Fewer bees were disturbed, fewer bees took flight, and the swarm tended to fall into the catching bucket with a ‘plop’ and more intact, with queen not taking flight as often either.  Picture here, bees in a swarm with their little hooks holding them together,  a strike up, simply causes all bees below to loose their grip and fall still adhearing to each other, and with minimal violence.  

When using the catching bucket on a pole, I would recommend a rapid upwards movement of the bucket striking the tree to perhaps be more successful.  This can be difficult to do at 20 feet, so a rod extending from the side of the bucket upwards, to use as a guide that one can lean against the branch will add some stabilization and accuracy when performing the upwards strike.

Best Wishes,

Joe Waggle ~ Derry, PA  
‘Bees Gone Wild Apiaries' 
1870 Waterloo, Iowa - “An army of bees are said to have swarmed into a church, in Gloucester, Mass., last Sunday, during divine service, but retreated when the sexton shook the contribution-box at them.”
http://pets.groups.yahoo.com/group/HistoricalHoneybeeArticles 


      

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