Syndicated content and search engine indexing

Published and later removed, 404 and meta noindex

[johoney]

My site has a content syndication arrangement with a very authoritative and well known news service.

We get a daily feed of articles that are published on my site and after an initial period (around 1 week) the articles are removed from my site.

We find that search engines index the content and (no surprise) get a 404 when its removed from our site.

Is it better to meta noindex/follow these articles so as not to annoy search engines with lots of missing pages? My feeling is that search engines could claim that we are giving searchers a bad experience if they see the link in SERPS but then get a 404.

Cheers - JoC
p.s. donate to Haiti relief fund on doctorswithoutborders or Red Cross

[physics]

Is there any way (within your agreement, or by renegotiating) that, after that first week, you can keep the first paragraph and link to the full story on the news service's site instead of totally removing it?