There is precedent here in Washington state.
RCW 9.41.300: Weapons prohibited in certain places ? Local laws and ordinances ? Exceptions ? Penalty. ... the local legislative authority shall provide either a stationary locked box sufficient in size for pistols and key to a weapon owner for weapon storage, or shall designate an official to receive weapons for safekeeping, during the owner's visit to restricted areas of the building. The locked box or designated official shall be located within the same building used in connection with court proceedings. The local legislative authority shall be liable for any negligence causing damage to or loss of a weapon either placed in a locked box or left with an official during the owner's visit to restricted areas of the building.
I can attest, having done jury duty in King County in 2006, that it's a pretty easy, painless thing. I showed up at entrance, and calmly told the security folks that I had a firearm I needed to check. The security folks said to the uniformed deputy on duty there, "We need an escort". That's the polite euphemism they use at the King County courthouse. Doesn't "scare the horses".
The deputy head nodded and motioned for me to come over to him. I waited there a minute or two, a second deputy came down, I walked with him down to a secured room, they gave me a tag with a number on it for the key, and I locked up my firearm. The deputy asked me if I was doing jury duty, and I told him I was. He said I should take off my holster as well because, in his words, if people in jury room see an empty holster someone will freak out and call us.
The deputy kept the key, I kept the card, and he escorted me back to the entrance. The key remained with the deputy there at the entrance desk, I passed through the metal detectors, and entered the courthouse now unescorted. Took all of but a few minutes. Same drill in reverse when I went out for lunch and left for the day.