Nobody asked for it, but here it is anyway: A way to perform a tracebox, similar to traceline but with a full sized object, without engine extensions. Caveats: The emulation of a trace is not perfect; it can throw a false negative in the case where the trace travels through a small but non-zero vertical distance. The test has been designed to prevent false positives. In addition, it's quite expensive in QC operations, although look to the previous post to see whether you should care about that.

"Your mother's a tracer!"
So, the key to being able to trace is, strangely enough, flying monsters. Most of the box-tracing which the engine performs is during physics updates. This makes them unsuitable for testing traces "on-demand", since you have to give control back to the engine first. However, monster movement is performed in discreet steps, moving instantly from one point to another using the walkmove function. Flying monsters have the additional advantage of not being bound to the ground, so we create an entity with FL_MONSTER and FL_FLY set to perform our trace.

The carrot and the stick
It's important to understand exactly what causes a flying monster to change altitude. Every time walkmove is called, the moving monsters decides if it is at the right height, too low, or too high. Accordingly, it attempts to trace a move straight forwards, forwards and up by 8 units, or forwards and down by 8 units. It makes the decision based on the height of its enemy relative to itself. So to control which way our monster goes, we need an enemy entity whose height we can set. This is quite like the carrot on a stick you wave in front of a donkey to guide it onwards, and I shall refer to it as the "carrot". Since our donkey can fly, it will be named "pegasus".

Running the course
The first problem is that we can only climb 8 units at a time. The solution is to call walkmove repeatedly, dividing up the trace up into segments, where each segment has a z component of 8. Since it is unlikely that the trace will have a height exactly divisible by 8, we need to perform an initial run which stops less than 8 units away from the target height, then reset the origin of pegasus so that it lies on the path of the trace, 8 units from the target height. Full marks for whoever spots the tricky boundary case of this method.
Preach's Pro Tip: You can use this trick of calling walkmove more than once to get regular flying monsters to ascend/decend more rapidly!

Jumping the fences
The next problem is what happens when the movement of the pegasus gets blocked. What few people realise about walkmove is that if the trace is blocked, the monster doesn't move at all - I personally imagined it would move the monster as far as it could before being blocked. But if the movement with vertical motion is blocked, the code does attempt a move with no vertical motion before giving up. This could create false positives easily. To make sure that pegasus is properly jumping the hurdles, check that the height of the pegasus changes from one walkmove to the next. This is the simplest test, as it doesn't matter if the trace is going up or down. Of course, you shouldn't do this if the trace is truly flat!

The final straight
A big problem arises if you want a trace which isn't flat, but rises/falls less than 8 units - a shorter distance than a single walkmove. This is the corner case astute readers may have caught earlier. It might be tempting to give yourself a "run-up", to trace from a position behind the desired origin, through the desired start to the finish, so that this extended trace has the right height, and accept the false negatives that the longer trace might cause. The problem is that this might actually cause false positives!

If the pegasus starts within a solid part of the bsp (or possibly other object), then it seems to skip through without colliding. As traces get closer to 0 height, the pegasus takes a longer and longer run-up until it is exceedingly likely it will be outside the level. So instead, the best solution I could come up with for this case is: Increase the height of the pegasus by the desired height, adding it to the maximum height if the trace goes up, and the bottom if the trace goes down. Then perform a horizontal trace. If you look at the 2-D side-on view of the trace, this is effectively taking the rhombus which would be the exact trace, and replacing it with the smallest rectangle which could enclose it. 

You can lead a horse to water...
Through the steps in the previous post, we've built a reliable tracebox which reports few false positives and no false negatives. So it's time for a little nicety - stopping splash noises. The splash noise occurs when the pegasus crosses a water boundary, but since the pegasus is an imaginary beast, no noise should occur. To avoid it, we test for water by performing a regular traceline from start to end. If trace_inwater i set, then we add 1000 to the height of the trace_start and trace_end, then subtract 1000 from the mins and maxs of the bounding box(thus the box remains in the correct place. Although you could construct a map where a splash would still occur, I think it's unlikely to arise in actual maps.

Photo finish
And that's it. I'm sure I can hear you saying "That's all very well in theory Preach, but it sounds like a bitch to actually implement!" Fear not, for here is a qc file with just such an implementation. In this version, the carrot and pegasus are globally allocated entities, which reduces the overhead of spawning them each time you want to use the function. This could be changed if entities are at more of a premium than function cost.
http://www.btinternet.com/~chapterhonour/tracebox.qc
As a final warning, remember that the trace results are invalid if the tracebox starts outside of the level. When determining this, you have to account for the 3 hull sizes which quake supports. Work out which hull the tracebox fits to, and fit THAT inside the level. This almost always means that you need a player sized space!