There are very few things that one can say about
swarms that would apply to all swarms and all cases,
but I'd suggest that the branch might have been supported
by a helper while you sawed it off, and then placed it
(with care) on (or in) the hive body or transport
container.

Any branch that you can "shake" you can also saw off
with a bow saw (a handy item to bring on swarm calls).

Of course, finding someone to hold the branch can be
a problem, even when it can be shown that the swarm
is harmless at close range.  That's why you need a
250 coil of rope to toss over another branch and use
to support both ends of the branch to be cut.

But swarms on branches are never there for the long
term, so quick action is required before they get
organized, and fly off to their selected site.

If the branch is low, I will take one of a collection
of cardboard boxes, and "enclose" the swarm with the
box before shaking the bees into the box.

I rarely bother with woodenware hives for swarm
collection.  Cardboard boxes with a frame of old brood
comb jammed into one end are all I use.  Much lighter,
and easier to hoist up to the swarm with yet more
rope (passed through holes cut in the cardboard).

I prepare boxes by taping some window screen over a hole
I cut in one flap of the box-top for ventilation.  Then
I capture the swarm and tape the box closed.  I never give
them the option of leaving.

When I "shake" branches, I do it with a very hard swing of
a 4-lb short-handled sledge hammer.  The impact needs to
be both abrupt and excessive if you want to dislodge all
the bees (and the queen) in one swell foop.

        jim

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