What About Capacitance Meters?
Simple capacitance scales on DMMs just measure the capacitance in uF and do not test for leakage, ESR (Equivalent Series Resistance), or breakdown voltage. If the measurement comes up within a reasonable percentage of the marked value (some capacitors have tolerances that may be as much as +100%/-20% or more), then in many cases, this is all you need to know. However, leakage and ESR frequently change on electrolytic as they age and dry out.
Many capacitance meters don't test anything else but are probably more accurate than a cheap DMM for this purpose. A meter of this type will not guarantee that your capacitor meets all specifications but if it tests bad - very low - the capacitor is bad. This assumes that the test was made with the capacitor removed (at least one lead from the circuit - otherwise other components in parallel can affect the readings.
To more completely characterize a capacitor, you need to test capacitance, leakage, ESR, and breakdown voltage. Other parameters like inductance aren't likely to change on you.