Domotica to the coil additional coils. This will increase the inductance of coils with constant parameters the remaining structural elements, and the variometer (coil with a movable core) - will shift both limit changes in inductance (top and bottom) upwards. When winding additional turns may be that they do not fit on the frame. Do not be tempted to use a finer wire than that used in the original coil, so as not to cause heating of the windings flowing through it current.
To the coil not having a core, add such. But remember that it needs to be made of such a material, in which the operating frequency of the coil does not occur losses in eddy currents. For an electromagnet operating on direct current, suitable solid steel core, for 50-Hz transformer - core, recruited from the blue plate in the higher frequency coils will have to use cores made of ferrites of different grades.
Remember that even with the same number of turns and other parameters of the coil of greater diameter will have a higher inductance. It is clear, however, that the wire for its production will need more.
The ferrite is manufactured with different magnetic permeability. Replace one ferrite core in the coil to another, which is the value of this parameter above, and its inductance will increase. But it will decrease the marginal rate at which this coil can operate without any appreciable loss in the core.
There are coilsequipped with special mechanisms to move the core. In order to increase the inductance in this case, slide the core into the frame.
A closed magnetic circuit, ceteris paribus provides a higher inductance than open. But try not to apply this decision in transformers and chokes operating in the presence of a DC component. It is able to podmanivaya and saturate a closed core, thereby, on the contrary, causing a decrease in inductance of the coil.