You can create a secondary replica of database with the same name on another Azure SQL Server, making the local database primary, and begins asynchronously replicating data from the primary to the new secondary.
ALTER DATABASE <<mydb>> ADD SECONDARY ON SERVER <<secondaryserver>> WITH ( ALLOW_CONNECTIONS = ALL )
Target server may be in another data center (usable for geo-replication). If a database with the same name already exists on the target server, the command will fail. The command is executed on the master database on the server hosting the local database that will become the primary. When ALLOW_CONNECTIONS is set to ALL (it is set to NO by default), secondary replica will be a read-only database that will allow all logins with the appropriate permissions to connect.
Secondary database replica might be promoted to primary using the following command:
ALTER DATABASE mydb FAILOVER
You can remove the secondary database on secondary server:
ALTER DATABASE <<mydb>> REMOVE SECONDARY ON SERVER <<testsecondaryserver>>