More than 67 Jovian moons? Wikipedia says that there are now 67 known moons of Jupiter. 

It got me wondering: is it really possible in our day and age that there are more, but we haven't observed them yet? 

On the other hand, there is a Jovian moon discovered as recently as in 2011, so I wouldn't be amazed if the answer was 'yes'.

Really though, choosing Jupiter for this question was a bit arbitrary on my part, as the same question can be asked for other more distant and bigger planets of our solar system, like Saturn.
Yes, there probably are more.

There is a minor problem of definition. Unlike the case for "planet", the IAU has not produced a definition of "moon". There is no requirement to be round, or have cleared an orbit. So any chunk of rock or ice that we can see orbiting a planet can reasonably be called a moon, and Jupiter has, over the years, picked up a lot of stuff: Small asteroids that it has captured from solar orbit.

It is likely that there are other, sub-1km sized objects in orbit around Jupiter, that we haven't noticed yet.

Juno is, as of 2016, in orbit around Jupiter. However her main focus of study is the planet itself, not hunting for moons. The recent moon discoveries have been made by terrestrial observations.