By Chris Cowherd, CTO.
The best thing to do is migrate your content to yournew.domains and do a 301 redirect (permanent) from old-domains.TLD. It's safe and maintains all of your Google love. Google is completely geared up for this scenario and it is documented on their site.
See attached checklist for a complete guide to migrating your domain.
Search engines don't count framed content as duplicate content because the URL of the frame tells the search engine the source, so an iFrame won't hurt their SEO. There may be security issues if the customer transitions to a secure page from an insecure one. A search engine will not attribute content inside the frame to the framing domain (yournew.domains). If it was that easy to hurt someone's SEO, a competitor could set up a site framing your site. If you are paranoid, see my blurb below on the canonicalURL tag.
<html><head><link rel="canonical" href="http://old-domains.tld/" />...</head>