I was asked the other day 'can we take cremains on a plane' and I figured this would make a good article :) So in short, the answer is yes, you can do so, however it's important to understand your individual airline's restrictions. Some airlines are quite lax on the subject where others don't allow urns to be a carry-on item.
But for many, the bigger concern is simply getting past security. For this, let's take a step back and understand the underlying concern many organizations (i.e. postal service) has with cremains. Generally it's not an issue with the emotional aspect but one of safety. Cremains is a rather abrasive substance and also has an electro-static element to it. If it gets loose, it is very difficult to remove from the environment if the environment is industrial in nature (like the inside of an airplane.)
As such, the primary concern for most industries that might deal with cremains is one of the cremation ash being secured in a seal-tight container. Coming back to security, as long as the cremains are in a seal-tight container they won't open it. They may still X-Ray it and handle it, but they won't open it as a general policy. However, if they can't determine to their comfort level the urn indeed contain ash, it won't be allowed on the plane. For this reason we suggest bringing documentation of some sort.
For smaller amounts of ash, the only consideration to make is make sure it's 'double bagged' so it won't get loose. We would suggest putting this in a clear bag so it can easily be inspected by TSA. This link and this link have some more information on the subject.
As always, comments and statements in this blog are meant as guidelines rather than legal advise.