When switching our website from HTTP to HTTPS, things went catastrophic:

• Page impressions went down from average 60 (peak 110) to below 10 (resp. per day).
• Traffic from search engines dropped to zero.
• In other words, we became almost invisible on Google.

What caveats may we have missed?

This is what we did:

• Using a commercial SSL certificate (i.e. no self-signed or CAcert)
• Using the exact same domain name as before (i.e. no "www." before and after)
• Using 301 redirects for each HTTP page to its HTTPS version
• Internal links are all relative URLs (before and after)
• Same content, except for chaging "link rel=canonical" URLs from HTTP to HTTPS
• Google webmaster tools don't show anything suspicious.
• robots.txt is unchanged, containts just two lines User-agent: * and Disallow: /wp-admin/ (The last one is a leftover. there is no Wordpress running. These are static, cleaned-up pages)

As far as I can tell, we did everything that is recommended by SEO blogs and other StackExchange answers (such as http://webmasters.stackexchange.com/a/68089/48957).