Save contacts - Save contacts app provides features through which users can select the desired data to create the backup in a variety of different formats.
iMazing - iMazing lets you transfer music, files, messages, apps and more from any iPhone, iPad, or iPod to a computer, Mac or PC. Manage and backup your iOS device simply without iTunes. (was DiskAid)
SIM Contacts Manager - SIM Contacts Manager app offers features that let you insert your sim card to your mobile phone to manage, edit, add, and delete your contacts right at your fingertips.
Blackra1n - (This is an OUTDATED jailbreaking method.)
X-Transfer - X-Transfer is an app by WebToGo that comes up with features to help you in performing data transfer between your smart devices in a few simple steps.
checkra1n - Jailbreak for iPhone 5s through iPhone X, iOS 12.0 and up