In a sea change from fears that gripped the region on the day after last June's Brexit vote, high-rated euro zone government bond yields rose briefly in early trade but some end-of-month buying pushed them back down as the session wore on.
"Today is a big day for the history books but it seems the market is not bothered too much by the triggering of Article 50," said Commerzbank strategist David Schnautz.
Germany's 10-year government bond yields edged a touch lower to 0.37 percent on the day and most other high-rated bonds were flat to 1 basis point lower.
The yield on Portugal's 10-year government bond yields, which normally rises in uncertain times, fell to its lowest level since early January at 3.72 percent, down 4 basis points on the day.
Schnautz attributed buying of euro zone government bonds to end-of-month flows, when many banks and insurance companies look to shore up "safe" assets ahead of having to report on the make-up of their balance sheets.
This is a different scenario from June last year, when 10-year German government bond yields dropped to minus 0.16 percent on the day after the Brexit vote and South European countries such as Portugal saw their government bond yields spike.
Analysts cited a strengthening euro zone economy and a higher inflation expectations as the main cause for the relative calm this time round.
"A mixture of good data seems to be proving the European economy is doing quite well," said DZ Bank strategist Daniel Lenz, pointing in particular to a survey on private sector activity released last Friday.
Businesses across the euro zone marked the end of the first quarter by ramping up activity at the fastest pace in almost six years to meet burgeoning demand, a survey found.
This is the latest in a string of data releases that suggest returning growth and inflation in the euro zone, a very different picture from the one predicted by many when Britain voted to leave the EU in June last year.
Yields came under some upward pressure after the US Federal Reserve vice chair signalled on Tuesday that two more rate hikes are on the cards this year, soothing concerns that inflation and growth expectations in the world's richest country may have been overdone.
Stanley Fischer said two more rate hikes this year "seems about right", pushing 10-year US government bond yields higher.
"The possibility that all in all there could be three rate hikes this year could be a trigger for higher yields today as well," said DZ Bank's Lenz.
US President Donald Trump's failure to push through a healthcare bill sparked concerns that he may struggle to go through with infrastructure spending promises, thereby potentially reducing expectations for growth and inflation in that country.