It depends on who you are buying from 🙂 
There is now a Harmonised Standard, EN 50581:2012, that may be used to demonstrate compliance with the RoHS Direcitve and this sets out a four stages process:
Determine the information needed 

• Collect the information 
• Evaluate the information with regard to its quality and trustworthiness 
• Review the technical documentation to ensure it remains valid

The standard doesn’t actually tell you how to define “sufficient quality and trustworthiness” – the manufacturer will have to do that themselves and the level required will depend, in part, on the risk of a restricted substance actually being present in the part.
Also, worth reading the Commission’s FAQ, if you haven’t already: 
http://ec.europa.eu/environment/waste/rohs_eee/pdf/faq.pdf

• Franco Costantini. Field Services Manager Europe at CSA Group — MBA, M.Res, M.Eng

  Hello, 
  reg the WEEE regulation, I don’t think (please tell me if i am wrong) it is possible to verify the effective compliance to it. One could probably verify if a manufacturer joined a producer take back scheme or something like that, but I suppose it is really difficult to verify for example if the waste generated from its products is taken back, processed, accounted for, disposed accordingly etc…

• Tony Stanley. Regulatory Engineer (American Dynamics) at Tyco Fire & Security

  There are no real requirements for components on WEEE, it merely states that the ‘product design should take recycling into account’. You make available ‘information for recyclers’ which is usually the location of any annex II items (Mercury, batteries, PCBs etc). Not sure what the annex is for the new WEEE directive, but seems to be the same list. WEEE is really about the producer funding recycling.
  Regarding RoHS, it does not apply to components, which is an important concept that components are neither compliant nor non-compliant for several reasons. You do need to know their RoHS status or when their ‘compliance’ might go out of date, especially if you hold stock for more than a few weeks. RoHS applies to finished goods when you place them on the EU market and it is a changing regulation with exemptions expiring and new materials to be added in future.
  To answer your question, the main approach specified by the RoHS-2 directive is to request or commision a test report. A component (in your product on the market) with a suitable test report is presumed to conform, although you should judge the appropriateness of the test report, recent? traceable to the item? etc.
  A common practice is to use XRF screening which for about £30,000 can detect element concentration, but it maybe inconclusive and more detailed tests require specialist labs. It will also not be suitable for certain items and exemptions (eg Mercury in lights is limited mass per light, not a concentration).
  You don’t need a test report for everything if you follow EN50581, but you need a material risk approach as well as a supplier risk approach. These are the difficult parts.

  • Tony Stanley Regulatory Engineer (American Dynamics) at Tyco Fire & Security

• I should add that there is no special allowance for complex sub-assemblies, but they are more difficult to deal with and test. However a test report is still apparently acceptable, but rare. I would be looking for a supplier to provide a material declaration with exemptions listed, a declaration listing EN50581 as a compliance approach (definately required if the item is already CE marked like a PC graphic card), or a brute force 100% component test reports. Additionally membership of substance database scheme by the suppliers will keep them informed of the current and future requirements, which is half the battle. 
  Just asking for these things can add significantly to your diligence. I found a LCD module supplier providing a declaration with no exemptions, when I asked if they used a Mercury free backlight a test report appeared showing the exemption was ‘in spec’.