There are a growing number of resources dedicated to improving web archivability, including tools, examples, and additional recommendations.
Vangelis Banos' web service Archive Ready provides an automated evaluation of some aspects of web archivability, based on a novel framework he proposed in a 2013 research paper. As is the case with accessibility, there are limitations to what archivability issues can be detected using automated tools.
Bing Webmaster Tools
Though built primarily to facilitate search engine optimization, Bing Webmaster Tools provides a number utilities that can help improve archivability including: site-level indexability reports, site-level HTML correctness scanning, inspection of individual webpage indexability and embedded metadata, reports on the discoverability and legibility of sitemap(s), and robots.txt testing
Google Search Console
The Google Search Console is another suite of utilities designed for search engine optimization that may also help improve archivability. The set of relevant features overlaps partially with that of Bing Webmaster Tools: site-level indexability reports, site-level reports on embedded metadata, reports on website usability on mobile devices, managing XML sitemap(s), emulating crawler access to a given webpage, robots.txt testing, individual webpage embedded metadata testing, and individual webpage mobile usability testing.
Internet Archive Wayback Machine
Though web capture and access technologies may vary somewhat across web archives, plugging a web address into the Internet Archive Wayback Machine and clicking around can provide a quick sense of possible barriers to the archiving or re-presentation of your content.
Columbia University Libraries guidance
As part of their 2013-2015 Web Resources Archiving Collaboration grant from the Andrew W. Mellon Foundation, Columbia University Libraries developed guidelines for preservable websites in particular for outreach to web builders whose content they are archiving.
National Library of Australia guidance
The National Library of Australia produced some early, now archived, web archivability guidance in 2002 titled, "Safeguarding Australia's Web Resources: Guidelines for Creators and Publishers". They also offered a companion 2001 document titled, "Managing Web Resources for Persistent Access" that focuses more specifically on website content organization and link persistence.
Portuguese Web Archive guidance
The Portuguese Web Archive's 2010 "Recommendations for authors to enable web archiving" offers categorized and prioritized tips on many dimensions of web archivability.
UK National Archives guidance
The UK National Archives offers extensive and up-to-date guidance on how to make websites more archive-compliant. The documentation is very detailed, includes many examples, and should be considered a more generic resource beyond the intended audience of UK government webmasters.