I don't think there's anything even remotely reliable for this, but maybe others can clarify.
It is unclear from your question whether you are interested in telomere lengths or telomerase. Telomerase is a molecular complex (containing an enzyme 'hTERT' and an RNA 'TERC') that extends the length of telomeres.
If you are referring to telomere lengths, there seem to be biological kits to measure these (google 'telomere length assay'). You probably won't be able to use these lengths to determine age. As far as I know, the correlation between telomere length and organism age is still very much controversial. If you take some cells from a human and culture them in vitro, the telomeres will shorten a bit at each mitosis, until eventually the population will senesce (stop dividing). Just because this happens for an individual cell line, however, doesn't automatically mean that older people will have shorter telomeres. My (very limited) understanding is that stem cells / progenitor cells within an organism express telomerase, so their telomeres are maintained at "full length", or perhaps shortening at a slower length. When a normal (non-stem) cell population in the body senesces, the stem cells/progenitors can be used to spawn fresh cells, where the telomere clock is effectively restarted. Some studies, like this one, have found that there is some correlation between age of the organism and the number of times a population of that organism's fibroblasts can undergo mitosis in culture (which presumably reflects telomere length). However, other studies, like this one, do not find a correlation, which would suggest that telomere lengths cannot be used to ascertain age.
If you are referring to telomerase, there are at least two ways you can investigate this from a bioinformatics perspective - you can attempt to quantify the amount of the hTERT protein in a sample (e.g. analysing mass spectrometry data of a protein digest), or you can attempt to quantify the amounts of hTERT mRNA and/or TERC in something like an RNA-Seq experiment. As above, however, this is highly unlikely to help you establish a person's age.
Is there a bioinformatic/computational biology angle to this question? If not, this isn't the appropriate forum.
It's offtopic. Bio_X2Y has posted a reasonable enough answer not to warrant further discussion I think.
I would guess the poster can't answer this question until he/she gets an answer :) The answer could be that there's a pure biological test, or perhaps there's a bioinformatically-resolvable pattern in the analysis of a biological test like a GeneChip array.
I was definitely thinking a computational biology angle to this question. As suggested in the answer, different cell types would indicate different ages. However, if we could test a few of these cell types at a few time points and the person-to-person variance was low enough, we would be able to predict effective age. The computational aspect, would be to setup the experiments to optimize for the best precision. This is pointless if the tests just resolve every 20 years.