The tide on the Virginia coast rises and falls about 1-3 feet, twice a day, at the NOAA reference stations. Development along the shoreline is based on those predicted tides, including potential high water and waves from floods that have a 1% chance of occurring each year (the "100-year floods").1
In theory, however, an earthquake could generate a tsunami (formerly called a "tidal wave"), displacing water in the ocean and creating a sudden surge as much as 10-25 feet high on Virginia's eastern coastline. The risk of Virginia being affected is considered very low, because very few earthquakes occur near the passive margin of the eastern United States. No one paid much attention to the tsunami threat - until the disastrous tsunami in the Indian Ocean in December, 2004.
Norfolk became the first "Tsunami Ready" Virginia city (in January 2006). Norfolk's assistant director of Emergency Preparedness and Response was not worried about a tsunami, and thought that he would win the Mega Millions lottery before a tsunami affected Hampton Roads - but the risk to Norfolk is greater than zero. His evaluation of risk vs. reward was clear:2
tsunami risk - especially low on the Virginia coast
Source: National Oceanic and Atmospheric Administration (NOAA), National Geophysical Data Center - Natural Hazards Viewer
The threat is small, but real. On June 13, 2013, a storm (derecho) off the coast of New Jersey or an underwater landslide triggered a minor tsunami on the East Coast. On the Jersey shoreline, the tsunami was clearly observed. A breakwater that is normally 3-4 feet underwater was exposed, and three people were swept into the ocean from rocks that were 5-6 feet above sea level.
In Virginia, six hours later a tsunami was recorded by equipment. The water level gauge at Kiptopeke on the Eastern Shore recorded a maximum rise of 10 inches, occurring 12 minutes after the gauge at Chesapeake Bay Bridge-Tunnel recorded a 3-inch rise. Such a change, well within the normal 1-3 feet tidal change each 12 hours or so, caused no damage.3
change in water height at Kiptopeke during June 13, 2013 tsunami
Source: National Oceanic and Atmospheric Administration (NOAA) - TSUNAMI of 13 June, 2013 (Northwestern Atlantic Ocean)
In 2000, a scientific study of cracks at the edge of the coastal shelf suggested how a damaging tsunami could be generated near the Virginia coast, despite the small number of earthquakes in the region. Landslides occur along the continental slope, initiated by those rare earthquakes or excessive accumulation of sediments on the continental slope.
Potentially, warming of methane hydrates (natural gas) now buried in ice crystals in coastal shelf sediments could "bubble up" if warm ocean currents shift location, causing a landslide and displacing enough of the Atlantic Ocean water to cause a tsunami.4
If an earthquake did occur in the Atlantic Ocean, it would need to be near the Virginia coastline to trigger a tsunami that could flood Virginia Beach, Norfolk, or the Eastern Shore. Research that indicates even a 7.5 magnitude quake "must be located offshore and within 100 km of the continental slope to induce a catastrophic slope failure" has reduced fears that earthquakes in the seismically-active Caribbean might pose a risk to Virginia.5
Another unlikely-but-possible-so-be-Tsunami-Ready risk is that the Cumbre Vieja volcano in the Canary Islands could collapse. Such a landslide, even though on the other side of the Atlantic Ocean, could generate a 10-25 foot high tsunami on the Virginia coast.6
An earthquake in Lisbon, Portugal in 1755 generated a tsunami across the Atlantic Ocean; it could happen again - though research published in 2006 suggested that it might require 10,000 more years before Cumbre Vieja became unstable enough to threaten the East Coast of the United States.7
Canary Islands, far across the Atlantic Ocean from Virginia...
Source: National Oceanic and Atmospheric Administration (NOAA), National Geophysical Data Center - ETOPO1 1 Arc-Minute Global Relief Model
Tsunamis have already struck on the western edge of the Atlantic Ocean, though far north and south of Norfolk/Virginia Beach. Port Royal in Jamaica was hit by tsunamis after a 1692 earthquake. The Palisadoes sandspit sank, killing one-third of the residents - an indication of the potential impact to residents on the shoreline of Virginia Beach and especially Willoughby Spit in Norfolk.8
To the north, Newfoundland was affected by a tsunami in 1929.9
A hurricane may have generated a tsunami that devastated Assateague and Chincoteague islands in 1821:10
A worst-case scenario involving a tsunami in Virginia has occurred, but it was 35 million years ago. A bolide (comet/meteorite) hit the earth and instantly created a massive crater near what today is Cape Charles on the Eastern Shore. The impact sent waves as far as the foothills of the Blue Ridge, perhaps even washing over them. The wall of water across the Coastal Plain and Piedmont would have created massive devastation to forests and wildlife, in what might be considered statistically a a once-every-35-million-years event.11
(In the Hollywood movie Deep Impact, a comet slammed into the Atlantic Ocean and the waves washed up to the base of the Blue Ridge. The scene at the end of the movie, of a traffic jam getting swamped by waves as key characters race up the mountain slopes, was filmed on the Route 234 bypass in Prince William County - but don't look in Virginia for those mountains. Those hills were covered by ponderosa pines that grow in the western United States; the movie's final scenes were not filmed in Virginia.)
bathymetric-topographic digital elevation model (DEM) of Virginia Beach area, used to calculate tsunami inundation risk
Source: National Oceanic and Atmospheric Administration (NOAA), National Geophysical Data Center - Virginia Beach, VA 1/3 arc-second MHW DEM
damage at Willoughby Spit after 1933 hurricane
Source: National Oceanic and Atmospheric Administration (NOAA) Photo Library