Yes. There are several approaches.
The simplest is to treat cells with damaging agent and measure the damage remaining (as strand breaks or enzyme-sensitive sites) at intervals during incubation. Thus you can measure the kinetics of cellular repair after very low (‘physiological’) doses of DNA damage.
Another method is the in vitro repair assay – a biochemical approach which measures the repair capacity. A substrate is prepared, of cells treated with an agent delivering an excess of damage of the relevant sort for the enzyme of interest. An extract is prepared from the cells whose repair capacity is to be investigated, and this extract is incubated with the substrate, for 10 or 20 min. Breaks accumulate as the incision events take place. Rates of repair vary between individuals.
Also, inhibitors of DNA synthesis (hydroxyurea plus cytosine arabinoside or aphidicolin) may be used to block the resynthesis step of nucleotide excision repair, causing breaks to accumulate; these give a measure of repair capacity, since incision is the rate-limiting step. Some hints: Pre-incubate cells for 15-30 min before giving damage; do not incubate for longer than 20-30 min after treatment (as breaks do not accumulate linearly after that); beware of the rapid rejoining of breaks when inhibitors are removed (so scraping may be better than trypsinisation to harvest the cells).
"FAQ by Andrew Collins, Gunnar Brunborg and Jonas Nygren, 2006, NewGeneris FP7-project"