Most general-purpose oscilloscopes have an input that is both resistive and capacitive - the capacitance varies from 'scope -to- 'scope but is pretty much constant for any particular model:
- Resistor: 1,000,000 ohms
- Capacitor: 15-30 pico farads.
These two components appear in parallel, and should not vary much on different Y-channel sensitivity ranges.
Many mutltimeters measure capacitance crudely and may have trouble with these small capacitances. The \$1M\Omega\$ input resistor might also cause problems, either causing a reading failure, or degrading accuracy of the capacitance measurement.
The \$1M\Omega\$'s effect can be made insignificant by using a high-frequency test signal above 1 MHz. You generally have no choice with a multimeter capacitance measurement.
Even if you can measure the oscilloscope's input capacitance, stray capacitance of the connecting wires to your coil-under-test can cause some error, especially if they are long. A coaxial cable between coil-and-scope should not be used - its capacitance would dominate any you add. A BNC-to-banana adapter will add some capacitance as well.
If you are resonating a coil with capacitance, you can expect that any device meant to sense a signal will have some capacitance, which will differ from your oscilloscope measurement, and will shift resonance to a different frequency. In such a case, a variable resonating capacitor is used so that resonance can be tuned to a desired frequency in the final circuit.
simulate this circuit – Schematic created using CircuitLab