2009-10: Henri Kiviaho split the season between the U18 and U16 teams for SaiPa in his hometown of Lappeenranta and appeared in two international contests for Finland's U16 team. Kiviaho played nine games for SaiPa's U18 team, which finished last in the 14-team SM-Liiga, and was 1-5 with a 7.63 goals against and .834 save percentage. In eight U16 qualifying games he had a 4.20 goals against and .902 save percentage. Kiviaho was 0-2 with a 3.67 goals against and .925 save percentage in three U16 Division I games.
2010-11: Kiviaho played for the U20 and U18 teams in SaiPa. Italian junior national team goalie Andreas Bernard and Richard Ullberg, a mid-season acquisition from HIFK, handled the bulk of the goaltending for the SaiPa U20 squad. In eight games, Kiviaho was 2-3 with a 4.28 goals against and .873 save percentage for last-place SaiPa. Playing for SaiPa's U18 team in its unsuccessful bid for a spot in the SM-Liiga, he was 0-3 in four games with a 5.86 goals against and .881 save percentage. In U18 Division I play, he played in four games and was 1-2 with a 2.96 goals against and .921 save percentage.
2011-12: Kiviaho moved from SaiPa to KalPa Kuopio and was a workhorse for the club's U20 team. In 28 games, he was 16-11 with two shutouts and had a 2.78 goals against and .910 save percentage. He started all nine playoff games for KalPa as Kuopio reached the bronze medal game and he was 3-6 with a 4.04 goals against and .868 save percentage. Though he was not among the 11 European goalies in the final rankings by CSS, Kiviaho was selected by Dallas in the fifth round (144th overall) of the 2012 NHL Draft.
2012-13: Kiviaho played for KalPa's U20 team, appearing in 31 regular season games and starting all three playoff games for the Kuopio club. KalPa finished tenth in the 16-team league and Kiviaho had a 2.66 goals against and .904 save percentage. KalPa lost to Tappara in a three-game preliminary series. Kiviaho played all three games and had a 4.04 goals against and .867 save percentage.
Kiviaho is a big goaltender with terrific reflexes and athleticism but also with butterfly tendencies. He can be rather electrifying in the crease and make a good variety of saves. He skates very well and his lateral movement is exceptional. He covers the low part of the net well and tries to emulate Pekka Rinne in terms of acrobatics, but he is very, very far off from that of course. He is displaying more patience in the net and is not overplaying cross-ice passes as much. He needs to improve his consistency, the technical aspects of his style, and his stickhandling.