Of course you can perform shimming in solid state NMR.  It's a standard for a number of techniques where high-resolution SSNMR is required.  Usually most of the line widths  are hundreds or thousands of hertz but those are the summation of the different crystallite magnetic field environments in the sample that are are being summed over.  If you are interested in a C13 compound were you have to 10Hz crystallite resolution and you are performing a line narrowing technique that will give you true T2 information then you need to shim.  Shimming can be performed using an liquid filled SSNMR rotor or for static samples a capsule.  Easily done as long as the spectroscopist is care about sample placement and orientation.  

Usually, If you are looking at powder patters that are tens to hundreds of kilohertz such as quadropole nuclides then there is not much call for worrying about shimming.  

This really depends on the experiment that is being performed.  Many SSNMR spectroscopists will know which system they are observing and can tell whether or not shimming is necessary.  

The line widths of NMR signals from lipid membranes and other liquid crystals can be quite narrow with MAS, whereas there is little or no chemical shift resolution with  a static sample. Take a look at my early papers, such as the "Why Sonicate?" paper in JACS. The real issue with shimming a MAS probe is that the shims are designed for a sample that is spinning around the magnetic field axis and when the sample is spinning at the "magic angle", the shim fields are mixed and it can be extremely difficult the get a field homogeneous enough the measure the natural line widths of the samples.

Article High-resolution proton and carbon-13 NMR of membranes: Why sonicate?

We are doing protein SSNMR and we usually shim with a spinning sample of adamantane just before starting a session on a protein sample. 

Thank you very much Jeffrey and Tobias...

Of course you have to shim in solid state nmr, but most often it is done manually as compared to auto shimming on a lot of modern liquid state probes. I believe Bruker may be working on a topshim protocol for solids but I may be wrong.

Can anyone share any tips on shimming on Adamantane?  I find it's not very responsive.

Depending on your MAS rotation rate the Adamantane may be undergoing spin diffusion.  Look up Ernst, Verhoeven and Meier - JMR 130, 176-185 (1998) for C13 spectra and self-decoupling - slower MAS (5kHz produces a narrow line and therefore more responsive to shimming).  For 1H domain and shimming look up Gil and Alberti SSNMR 11, 203-209 (1998) higher speed (15 kHz) produces a narrower and more responsive line.

Here is a little jewel from Bruker on the "proper Bruker" method for setup of a CPMAS C13 experiment on Adamantane.  It may be of help with your question...

Bruker SB MAS Manual - NMR Guide & Encyclopedia

6.5 Adjusting the Hartmann-Hahn condition on Adamantane and fine-shimming

Thanks to the 

INSTITUTO DE QUÍMICA FÍSICA ROCASOLANO

Departamento de Química Física Biológica

Madrid, Spain

http://triton.iqfr.csic.es/guide/nmr/sbmas/sbmas6_5.html