Is the EMP threat to the power grid supported by physics? Every once in a while I come across some article saying that our modern power grid could be knocked out of commission for up to a year by an electromagnetic pulse.  I'm skeptical of such warnings.  
Is there any good scientific research that addresses this purported threat?

How is this off-topic?  What other science would address this question?  It's a legitimate, and important question.  It is, in fact the ethical duty of the physics community to have answers to these kinds of questions.
 A: It’s more of an engineering question than a pure science one, so a place to look for research is the IEEE. There’s a lot there. For example, the first hit on my search was “Unaddressed threat to power grid infrastructure: Electromagnetic pulse” (IEEE 2016) with abstract:

Detonation of a nuclear weapon at high altitude, produces high
  magnitude Electromagnetic Pulse (EMP which will cover the extensive
  geographic region within the line of sight of detonation. This high
  magnitude EMP when interact with sensitive electronics network, has
  the competence to produce extensive and long eternal disruption and
  destruction to the critical power infrastructures like power grids
  that is sufficient to underpin the fabric of an economy. A single EMP
  attack seriously degrade or shut down a large part of the electric
  power grid in the geographic area of EMP exposure effectively
  instantaneously. In this paper, impact of EMP on power grid has been
  critically highlighted and an effort of understanding about the
  interaction of EMP with electrical power infrastructure has been made.
  Moreover, EMP as a threat to national security has been underlined and
  techniques of mitigations are also recommended.

See also “Electromagnetic Warfare Is Here” (IEEE Spectrum 2014) and the rather chilling work in “Electromagnetic Warfare and the Cybersecurity Threat” (IEEE 2017)
A quick survey search didn’t find any published research arguing that there is no such effect. 
From the science and policy side, the National Academies have published “Terrorism and the Electric Power Delivery System”, which addresses the issues of recovery from a number of scenarios, including what extends recovery time. 
Briefly, a localized outage recovers much quickly if it can get power, people and parts from adjacent areas. It’s much harder to recover organically, without that support because the adjacent areas are out. Additionally, there are only a limited number of spares for certain critical, but long lasting, pieces of infrastructure. It would take a very long time to manufacture large numbers of those, especially without power. 
A: Yes, there was a quite significant solar activity event in 1859, when the electrification of our cities was still in its infancy.
The event heavily ionized the upper atmosphere, and induced strong currents in the ground, to the degree that telegraph operators could communicate over landline with their batteries disconnected (the power being supplied by the ground).
Such an event would wreak utter havoc today, on a global scale.
