There are ways to detect an embolism and there are screenings that will not show one at all. X-rays are not effective to diagnose an embolism but can rule out other root causes for symptoms. A pulmonary angiogram is one of the most effective diagnostic tools there is for finding an embolism. Also, an MRI can detect one. An ultrasound is another effective way to find an embolism.
Embolisms are not easy to detect in a regular checkup. They are made of blood and blood doesn't show in xrays. It is usually when one is suspected that it can be screened for and is often found by way of an ultrasound, angiogram, or other means.
Anyone who suspects they have a blood clot should seek medical help immediately. Then measures can be taken to diagnose and, if necessary, disolve it before it causes great, possibly irreversible, damage.