I have an idea which I'll try to put into writing but it might not be obvious what I'm driving at. I actually had a couple of thoughts on this but one may be more sensible than the other.
Up and Over
My initial thought was that one of the trains, probably the 200 km/h one as it would already likely be a streamliner, would be designed in such a way that it's front is like a ramp and it has rails built into the ramp which run along the track in front of it. These rails continue over the carriage roof and the rear of the train look like the front. The oncoming train could then be forced to run over the top of the fast train. This does however require that the train that goes over is able to climb an unrealistic gradient although oncoming speed may assist. It also assumed that there are no overhead electricity cables but that the train above is able to continue to proceed without a "third rail" either.
Shall we dance?
As an alternative to the up and over method, I came up with something that could actually work. On a traditional track, you'd place the 100 km/h train in a siding and have it wait until the 200 km/h train had passed. I realize that this can't work because it requires you to know where the siding would need to be.
However, when you consider what a train requires, it is essentially rails on which to run. Now, imagine that each train is carrying some sort of short section of rail at its front which is angled from the right to the left of the track. When the two trains come close enough, these angled tracks collide and are forced into the rail bed. This causes the left-hand wheel set of each train to jump off the left hand track and the right hand wheel set is forced onto the left hand rail. This effectively derails both trains simultaneously causing a massive accident. However, if the tops of each train were designed to carry some sort of rail / tube on top of the train with some sort of interlocking arm, the weight of each train would be carried by the other.
Each train would hold the other up, a little like a spinning ballerina is supported by one of two feet and by a dance partner at the top of their arm, outstretched above their heads. Both locomotives would progress along the same piece of track but using just one rail each, each locomotive offset and supported by the other.
Once they had passed each other, an assembly at the rear of each train could "re-rail" the wheel sets back to their original location which would effectively by a mirror of the assembly at the front of the train.
Hopefully this makes some sense. If not, I could possibly try to sketch out how it would look.
Edit Added sketch
Edit 2 — "Budge Over" trains
You could potentially re-design the trains to allow the "shall we dance" method to be a little less severe. Instead of forcing the trains to jump to the opposite track, design the trains to have an angled cab with looks like a triangle when viewed from above. Along one side of the train, have interlocking "rails" which would interface with each other, shoving the oncoming train onto the side of the opposing carriage.
Redesign the wheel sets so that they had one fixed set of wheels and one "sprung" set which were floating so the trains could continue to run one wheelset on a single rail but the other would float in free air under the train.
This would effectively allow trains to "slither" past each other. Whilst this refinement to the design probably makes the solution a little more realistic, it does remove some of the grand drama that the "Shall we dance" method has.