Yes, the usual multimeters do capacitance measurement and inductance alternating current. But the way to measure capacitance at a constant current is. You can use the parameter "time constant of an RC circuit":
Charges the capacitor to a known voltage, then discharged him to a resistor with known resistance. At the time of connection of the resistor it is necessary to start the stopwatch, and when the voltage on the capacitor will drop by about two-thirds (exactly - to the level of 36.8% of the original), the stopwatch will show the value of the time constant (Tau, in the formula above). Knowing Tau and resistance, this formula is elementary, the calculated capacity.