Is there any easy way to align two handles when using the pen tool?

Kurt,

It was a pleasant surprise to see the GIFs appear out of nowhere, especially the second one.

Femke, can you show your settings in the Smart Guides section of the Illustrator preferences?

@barbara_a7746676  Thanks.  I wanted to avoid the grid since it's restrictive and defining it adds an extra step, but that may be the way I'll end up going. 

@Kurt Goldand @Jacob Bugge  Thanks.  You're correct in that I can snap one of the handles, the handle under the cursor, to a guide, but not the opposite handle.  More troubling is that I can't emulate what you showed with the smart guides.  I can get the handle under the cursor to interact with anchor points, the bounds of the curve and the centre of the curve, but not with handles. 

Femke,

From now on you may find it hard to resist the temptation to start with an asymmetrical curve, just for the sheer joy of using the exquisite Smart Guide solution by Kurt.

Your first sentence makes me curious: This is related to drawing symmetrical curves.

If you wish symmetrical, the Anchor Points will need to be aligned (relative to the relevant direction) to begin with, or the Handle lengths will be different if the Handles are aligned. If the Handles are vertical orhorizontal, this can be done in different simple ways albeit less exquisite ways.

Direction Handles usually do snap to guides (and used to snap to them in older versions of Illustrator as well).

Also, direction handles are smart guides sensitive, but an extra step is required: You'd first have to drag one handle precisely onto the other handle to set some kind of reference point, then drag it to the desired position following the horizontal or vertical smart guide until the "Intersection" indicator appears.

You can turn on Snap to Grid under the View menu. That makes it easier to align the handles.