450 votesChad commented
I came up with a workaround that I haven't seen anywhere else. The object blur / mask method is better for allowing objects to be moved around with inner shadows following them (i.e. to update your interface design in the future). Nonetheless, I thought I'd post this method anyway in case anyone finds it useful.
(BTW, add me to the long list of people desperate to see inner shadow added as a standard feature...)
First, realize that an inner shadow of an object is logically equivalent to a drop shadow cast by the object's background. This alone might be enough to realize where I'm going...
Make a copy of the background (or if it's a plain white background, draw a white box). Remove the border. Make a copy of the object(s) you want to add the inner shadow to. After pasting, shift-select the background copy and use Subtract (ctrl-alt-s) to cut holes in the background. Then use CTRL-[ or CTRL-] as necessary to move the object(s) and/or background up/down layer levels until the drop shadow of the background covers the object.
If the original background itself had a border, then you'll have to position the borderless background copy *just inside* the border of the original background (zoom in a lot so you can line it up exactly).