I use plastic spring clamps to make a tripod, but for anything that is likely to need a more strurdy or permanent connection, I get the hot pointy thing out and add a short through-hole component lead I can clip on to.
For high speed probing I make up a coaxial spring setup for ground and testpoint out of wound through-hole component leads so that the probe can be slipped in.
For differential high speed probing such as USB HS speeds and above, it’s typically a jury rig with elastic bands and/or kapton tape to hold the bulk of the probe and judicious tip browser adjustment. If the signal is designed to run over a cable, I make up a very short M/F breakout to intercept the signal where I can probe.