Hello, A nice measurement is the low frequency BH curve. The basic setup is relatively simple, but you need some math to convert the measured properties back towards magnetic field properties.
You can find an example measurement setup at:
http://info.ee.surrey.ac.uk/Workshop/advice/coils/BHCkt/index.html
If your Digital Oscilloscope has integration together with XY mode, you can skip the integrator. You need the integrator to "undo" the d.../dt from the induction formula
Vind = n*d(flux)/dt, Vind = induced voltage [V] n = number of turns , flux = core flux [Wb, Vs]
With the same setup you can measure initial permeability, maximum permeability and saturation flux density.
If you want to use your ferrite cores in an EMC/filter application, you need to measure the small signal permeabillity (real part and imaginary part) versus frequency also. That can be done via measurement of the complex impedance versus frequency at small signal level. From the impedance you can find the inductance (also real inductance and loss inductance based on number of turns and core geometry). From there you can derive u' (the real "inductive" part of rel.permeability) and u" (the imaginary "resistive/loss" part of rel. permeability).
When you are familiar with AC network calculations (complex or real), you can determine impedance with your setup by measuring amplitudes and phase shift. Depending on your setup and frequency, you may need to correct your measurements for the input capacitance of your probes.