Kidge

Kidge is the Het ship between Keith and Pidge/Katie Holt from the Voltron: Legendary Defender series.

Canon
As of current time, the two characters haven't had many personal interactions in the show; however, Keith and Pidge seem to hold mutual respect for each other and can work well with one another.

Things were rocky, to begin with as Pidge's decision to leave to find her family in season 1, episode 4 (Fall of the Castle of Lions) was harshly criticised by Keith; so much so that Shiro had to step in to remind Keith that he can't force Pidge to stay with them. This was soon put behind them after Pidge saves the castle and says she no longer wants to leave the team.

Most other interactions shared between these two are seemingly positive. In season 2, episode 3 (Shiro's Escape) the team try to take down an unknown invader on the ship. At one moment, Pidge has the enemy dragging her along by her bayard with Keith running alongside her. They look to each other, both exchanging a quick nod before Pidge takes action and puts on the brakes to slow down the enemy giving Keith the chance to attack. This displayed that the two are capable of working together without the need for verbal communication which hasn't always been the case with other paladins.

Fanon
While one of the smaller ships in the fandom many still love the possible dynamic between Keith and Pidge. Having both at some point lost those close to them due to the Kerberos mission, fans love to imagine scenarios where the two communicate to one another over their losses especially so during Shiro's disappearance at the end of season 2.

A popular theme for the pair adopted by many in the fandom is cryptid hunters. It's not unusual to find the two characters working together in various fanworks and AUs looking for conspiracies, the mysterious and unexplained. This is most likely due to canon influences where both Keith and Pidge were finding strange phenomena and working on theories soon after the failure of the Kerberos mission however they were doing this likely before they even knew each other.

Whether romantic or platonic, fans love to pitch the two in general as really good friends in their fan works.