Which mysql collation is good for storing unicode strings?
The issue was with connection character set. After setting it to utf8mb4, it succeeded. One way is to add default-character-set = utf8mb4 to client or mysql sections of ~/.my.cnf.

UPD Before adding default-character-set to ~/.my.cnf I had:

&gt; show variables like 'character_set_%'
character_set_client    utf8
character_set_connection    utf8
character_set_database  latin1
character_set_filesystem    binary
character_set_results   utf8
character_set_server    latin1
character_set_system    utf8


And insert into t1 (f1) values ('') gave me:

ERROR 1366 (22007) at line 1: Incorrect string value: '\xF0\xA2\x84\x82'
    for column 'f1' at row 1


After adding default-character-set = utf8mb4 I have:

&gt; show variables like 'character_set_%'
character_set_client    utf8mb4
character_set_connection    utf8mb4
character_set_database  latin1
character_set_filesystem    binary
character_set_results   utf8mb4
character_set_server    latin1
character_set_system    utf8


And insert into t1 (f1) values ('') succeeds.