There are a number of testing protocols for carcinogenicity, each of which has its pros and cons. In terms of ease and cost of testing, that really depends upon which tests you are willing to do or are required to undertake and the purpose of the investigation. If you can get hold of it, have a look at the Handbook of carcinogen testing by Milman and Weisenburger, published by Noyes.
The Ames test has its flaws but is a fairly useful basic assay for carcinogenicity. You're right, there are a number of compounds it does produce incorrect results for, the classic example taught to every undergrad is Nitroglycerol, which is not a carcinogen, but often flags a +ve result. The other thing to consider are compounds that are not themselves carcinogenic (hence give a -ve result) but when metabolised produce carcinogenic metabolites. These procarcinogens will not be detected by Ames unless you can include cellular material from animal liver which should metabolise procarcinogens producing a genuine result.
Hope that helps
R