Approaching an ideal inductor
But I've not seen in the literature that a similar, dual trick, is used for inductors: to connect in series inductors of smaller and smaller inductance (and hence, generally speaking, of smaller and smaller parasitic effects), with suitable shielding.


This is a very common practice when designing bias tees. A bias tee requires an inductor that can block a wide range of frequencies, for example, 10 kHz to 20 GHz in one application I've worked on. So a low-value, but also high series resonant frequency (SRF), inductor is connected directly to the input trace to block high frequencies, while one or more higher-value (and lower SRF) inductors are connected in series to block lower frequencies. 

Here's a high-end bias tee taken apart:


You can see a fairly complicated network of radial coils, toroidal coils, and ferrite beads used to obtain wideband blocking.