Depends what you mean by "cheap". I don't think the $10 ATMega based ones will have a hope of measuring trace inductance, though they should be able to roughly measure a few pF of capacitance over a ground plane of a reasonable area trace. Cheap handheld ones are not much better, especially for measuring inductance.
The pricier handheld ones, with Kelvin probes, have a chance. Mine (an actual LCR bridge that measures in quadrature) has a 1nH resolution on the lowest range, and the reading seems stable.
You have not given much of a hint of the range of measurements required or what you are doing, but my guess is that it is a power application with fast switching edges. In that case you can infer the inductance by making measurements of the voltage and current slope (assuming the inductance isn't actually killing your circuit- in which case the main issues should be fairly plain to see).