"such assurance" means having a guarantee or confidence about something. It implies feeling secure and certain about a particular situation or outcome. Full definition
With such assurances, private singles can set their minds at ease and do their homework on the top dating platforms for millionaires in a secure setting. (datingadvice.com)
The lack of such assurances has been a major complaint from the insurance industry and from state regulators. (fortune.com)
Nevertheless, even without such assurance the identification is a tempting one. (artnews.com)