Voice of Steel by Sean McMullen.
The Tynedale Journal ended with the sharp, shocking finality of an executioner's blade. Edward and William Tynedale had died in 1406 when the two-man culverin that they were testing exploded.
The protagonist Michelle (I'm not sure we ever learn her surname) sends messages to William Tynedale using a sword:
Then, on the 4th of April, 1404, William noted that he had bought a singing sword from some stallholder in a market, and that he intended to keep it under observation until it sang for him. The sword was Spanish in general style, and he referred to it as the Don Alverin sword.
The sword has become "entangled in time", and when Michelle speaks to the sword in the twentieth century the sound is transmitted to the sword in the fifteenth century. As you describe, Michelle uses this to send information to William.
However your recollection of the ending is awry as Michelle does meet William at the end of the story:
The Tynedale Brothers had taken my warning and published nothing. In private, however they had studied and worked like men possessed, and by 1418 they had completed a starship. The craft was about the size of a delivery van, but shaped a little like a pair of onions joined at their bases and resting on a lattice of satay sticks. It was all iron bands, barrel slats, copper sheathing, and oakwood rails. It had several arrowslit-style windows of quartz crystal, and by the smell of it the whole thing had been made airtight with bitumen. William gave me a tour of the interior. It was heated and powered by technology that could have won me the Nobel Prize for Physics every year for at least a decade, yet all of it had been built using materials and tools from fifteenth-century London. Carbon dioxide was split into oxygen and graphite by something mounted in a wooden washtub bolted to the roof. The drive was what had been described in the Tynedale Journal as an asymptotic boundary, generated by squeezing quartz crystals in an electrum collar at a precise frequency by … even now I cannot quite understand precisely how it works. The Tynedales did not either, they just followed the designs that I had given them as a different self. In this thing they had used relativistic time dilation to travel six hundred years in a few months, perhaps making the trip over seventy times, and stopping to take on fresh air and provisions each time.