On an Android phone, Cardilog reads your blood pressure from Health Connect, the Android feature that lets health apps share their data, and the readings you log in Cardilog are saved there too. So any monitor whose app saves to Health Connect works with Cardilog.
Of our picks, the Withings BPM Connect saves to Health Connect through the Withings app. To turn it on, open your profile in the Withings app, tap Settings, then Export health data to Health Connect, and turn on blood pressure before you tap Allow. We couldn't confirm on their makers' websites that the Omron, iHealth or A&D apps save to Health Connect, so check the app's settings before you rely on one of them with an Android phone.