There is no doubt that ovarian cancer is serious enough to offer tests. The problem is that the available tests are not reliable for screening. The forms of screening which are currently available are (1) a blood test and (2) ultrasound.
The blood test is readily available but only half of women with early cancer (the stage to catch it at for the best chance of a cure) have an abnormal blood test result. Even when the blood test comes back abnormal, it is not usually due to cancer, but a lot of anxiety is experienced while waiting for tests and results.
Ultrasound can show ovarian cancer, but this again is only really useful for screening if it is detected while confined to an ovary. Extensive research has shown that some ovarian cancers can spread while the disease is still microscopic (before it is visible with ultrasound or even the eye at surgery). Also when ultrasound shows something worrying, this can require an operation to sort it out. The research shows that each case of saving a woman’s life from cancer has not justified the number of operations (with their own risks and inconvenience) that are required in healthy women who turn out to have no cancer.
A lot of work is being done in huge studies around the world to improve screening, and at some stage a whole panel of blood tests will be available as a first step, with ultrasound as back-up if the blood test is abnormal. In the meantime, screening is not recommended for women who have no family history and are not unduly anxious. For those who want screening despite the lack of proof of effectiveness, it is reasonable to have either a blood test, an ultrasound or both. If you have both, the blood test should be ahead of the ultrasound so that raised blood tests can be addressed at the same time. However it is important to understand, the best a normal ultrasound can be said to provide, is reassurance of a lower incidence of ovarian cancer within a year.