The Independent has an article titled Heating cups of tea in microwave makes it healthier, says scientist. Does the research support this headline?
tl;dr- The research in question claims that microwaving can increase extraction of several compounds in tea; presumably, the news report assumes that these compounds are healthy. Despite the news report's wording, there's no conclusive evidence that the compounds extracted from tea are healthy, as stated in daniel's answer; this position seems to be shared by the researchers who describe the health benefits as "potential".
The quoted author publishes a separate paper discussing links to health benefits, but he also publishes a third paper that says that caffeine can have a negative impact on some people. The paper on potential health benefits also discusses potential health hazards.
Overall, the researchers are reporting that microwaving tea can help increase the amount of several of the chemicals of interest by about ~20% vs. their baseline preparation method. It appears that the researchers suspect that one of these chemicals, catechins, is potentially quite desirable, and this suspicion seems to form the cornerstone of their interest in human health.
Health benefits not claimed; merely potential
The paper that this news story is based on appears to be "Improved extraction of green tea components from teabags using the microwave oven" (2012), Quan Vuong et al..
Its abstract begins:
AbstractThe green tea (Camellia sinensis) catechins are strong antioxidants linked with potential health benefits. Based on previous studies, it was hypothesised that the typical household conditions for brewing green tea in a teabag – 200 mL freshly boiled water for 2–3 min, as per the manufacturers’ instructions – were not sufficient to extract all the catechins and that a household microwave oven could be used to improve the extraction.
So, from that first line, the authors claim that these compounds in green tea have "potential health benefits"; they don't actually make the claim that they do have health benefits.
Possible health benefits explored in separate paper
Separately, in "Epidemiological Evidence Linking Tea Consumption to Human Health: A Review" (2012) by Quan Vuong (and him only, as opposed to with a group of others as in the prior paper):
Tea has been widely consumed around the world for thousands of years and drinking tea is a daily habit for people of all ages. Tea is a major source of flavanoids, which have become well known as antioxidants. Tea also contains caffeine and theanine, which have been found to associate with health benefits. Many animal and epidemiological studies have been conducted to investigate the link between tea consumption and human health. However, common questions that arise about tea consumption include: whether all teas are the same, why drinking tea is linked with health benefits, how do the different ways of tea preparation impact on availability of tea components, how much and how long a person should consume tea to obtain health benefits, and whether there is any negative health effect associated with drinking tea. To answer these questions, this paper outlines the tea components and their link to human health, discusses major factors affecting availability of tea components in a tea cup, and reviews the latest epidemiological evidence linking tea consumption to human health.
An analysis and characterization of the links and evidence is beyond the scope of this answer, however it's probably sufficient to say that the paper includes:
Several epidemiology studies have reported the association between tea consumption and health benefits. However, the volume of tea required for obtaining health benefits is an area of speculation.
Since the original paper was about increasing the effective amount of chemicals released by tea by ~20%, the health benefits would seem to material if that ~20% is the difference in a volume that's less healthy vs. a volume that's more healthy; and as the authors say that'd fall into "an area of speculation".
In this paper's conclusions section:
Results from epidemiological studies were inconsistent and thus it is difficult to conclude how much of tea a day and how long a person should consume tea to obtain the health benefits.
Caffeinated tea can be unhealthy for some
The same author goes on to publish "Caffeine in Green Tea: Its Removal and Isolation" (2013) by Quan Vuong and Paul Roach, in which the abstract begins:
AbstractGreen tea is a rich source of the strong antioxidants, the catechins, but it also contains high levels of caffeine, which may cause negative effects in some people and this has led to a demand for decaffeinated green tea.
Since the first paper claims that microwaving increases the amount of caffeine released from 76% to 92%, it stands to reason that microwaving tea can make it less healthy for some.
Other potential issues
The second paper cited above, on the potential health benefits of tea, also discusses some of the potential negative impacts (beyond that of caffeine). Figure 1 from that paper shows a pathway to potentially increased cancer rates, while they also discuss the potential for the sugars in tea to contribute to diabetes. However, these effects are also quite speculative.
There is no conclusive evidence that tea is healthy in the first place, Wikipedia states that there has been a lot of research and not a lot of evidence to positive health effects.
The claim is that tea has some health benefits and that his microwaving method increases these benefits as it extracts more of these healthy components, my answer states that it's not proven that these components are healthy.
You might be able to separate out the researchers claim that microwaving can extract more chemicals from the tea (as it's another question) but I don't see him making the claim, it might have just been come from bad re-reporting. But on that note microwave assisted extraction is being used in other research.