Without knowing anything about your particular sample or what techniques you have access to, it is very difficult to be anything other than quite general.  

Firstly, you can never, of course, prove the lack of contaminants in an isolated compound but by using complementary, or orthogonal (different modes of separation) chromatographic techniques you can gain increasing confidence that certain things are absent. Your approach should be based on a knowledge of the origin of the sample (eg synthetic vs an extract) from which you may be able to anticipate the presence of certain contaminants, or classes of contaminants. 

If you are using an Evaporative Light Scattering Detector (ELSD) then you need to change the mode of separation by changing the chromatography column, for example C18 and HILIC should provide complementary separations in the case of LC.  Again for GC using a Flame Ionisation Detector (FID) you could try using capillary columns of different polarity eg BPX5 and BPX70 (SGE).

Another possibility would be to make a derivative and to chromatograph the product but unless your reaction is quantitative for all possible components and yields just one product, you run the risk of  introducing contaminants.

If you are interested in demonstrating optical purity then you will need to consider chiral chromatography.

Without knowing anything about your particular sample or what techniques you have access to, it is very difficult to be anything other than quite general.  

Firstly, you can never, of course, prove the lack of contaminants in an isolated compound but by using complementary, or orthogonal (different modes of separation) chromatographic techniques you can gain increasing confidence that certain things are absent. Your approach should be based on a knowledge of the origin of the sample (eg synthetic vs an extract) from which you may be able to anticipate the presence of certain contaminants, or classes of contaminants. 

If you are using an Evaporative Light Scattering Detector (ELSD) then you need to change the mode of separation by changing the chromatography column, for example C18 and HILIC should provide complementary separations in the case of LC.  Again for GC using a Flame Ionisation Detector (FID) you could try using capillary columns of different polarity eg BPX5 and BPX70 (SGE).

Another possibility would be to make a derivative and to chromatograph the product but unless your reaction is quantitative for all possible components and yields just one product, you run the risk of  introducing contaminants.

If you are interested in demonstrating optical purity then you will need to consider chiral chromatography.

Thanks a lot Charles for your comments. For proving the selectivity, we did also degradation studies, so we need to know whether the peak of our target compound was still pure (not contaminated); If the target compound was not UV active, and we do not have MS, so our choice is ELSD. For proving the target peak was still pure, we changed the chromatography conditions as your suggestions.

ELSD is a universal detector, but unfortunately does not provide much information in terms of qualitative analysis. I would call it a universal QUANTITATIVE detector.

If you had a pure reference standard and two columns with different stationary phase you could first analyze the pure reference standard on both columns and note the retention time on each column, and then confirm that your unknown analyte matches those same two retention times. However, this has several drawbacks:

1. The retention time of your analyte in sample matrix may change, compared to the retention time of the pure analyte.

2. To do this for more than a couple of analytes would be very time consuming and expensive.

3. Confirming the identity of the analytes via UV, NMR, MS, IR or some other qualitative technique would still be required at least once. It depends on how sure you need to be :).