The main march from City Hall to Stormont made its way along the six mile route via the Queen's Bridge and Newtownards Road in east Belfast.
Earlier around 2,000 Orangemen passed St Patrick's Church on Donegall Street, where a loyalist band played an allegedly sectarian tune on the Twelfth of July.
Up to 50 Land Rovers stationed along the flashpoint as the 20-minute parade outside the church passed off without incident.
Marchers were ordered to play only sacred music, including Abide With Me and Onward Christian Soldiers, from the Clifton Street to the Union Street junctions.
A protest held by the Carrick Hill residents' group was limited to 150 participants.
Following the parade, residents claimed a number of bandsmen broke the Parades Commission's determination. They said they heard the Sash being played before the end of the stretch, and claimed some bandsmen acted in a provocative way.
Frank Dempsey, chair of the Carrick Hill Residents' Group, said although the parade proceeded peacefully, the determination was "smashed".
"Some of the bands did stick by it. There's no problem with that there, but a number of them bands broke that," he said.
I'm glad it went peacefully... I think a degree of respect was shown that hasn't been shown before.
Father Michael Sheehan, parish priest at St Patrick's, said he did not hear the Sash being played, but said some of the bandsmen "seemed quite exuberant".
"There was a lot of vigour used in some drums and yes that could be considered as a bit defiant maybe," he told UTV.
The Parades Commission had also placed the music restriction on bands passing St Matthew's Catholic Church on the Newtownards Road.
However, it is understood the Sash was also heard being played near the venue.
Police say any breaches will be reported to the PPS.
The officer in charge, Assistant Chief Constable Will Kerr, said: "Throughout the day, police had an extensive evidence gathering operation in place and any breaches of the Parades Commission determinations are being investigated and will be reported accordingly."
The PSNI mounted one of the biggest policing operations for years in the city. Constable Will Kerr said the day "passed off in relative peace and calm" and praised the efforts which made this possible.
"These very real efforts, made by community representatives and Loyal Orders, supported by their political representatives, show a real willingness to achieve local resolutions. Hopefully this will create a more positive platform for dealing with sensitive parades in 2013," he said.
A significant police presence will remain on duty throughout the weekend to provide reassurance and support to local communities.
Constable Will Kerr
In a statement the Parades Commission said: "Any breach of a determination is a matter for the PSNI to investigate and those involved could be liable to prosecution.
"The Commission will take previous behaviour and any breaches into account in reaching future decisions."
On Saturday morning Orangemen from north Belfast lodges told UTV they were determined the Covenant Day marches would pass off peacefully.
"At the end of the day this is a celebration of the centenary of a wonderful thing that happened," said Leonard Walker.
"We do not want any trouble. We want this to be marked in the right way."
John Berry, who has been walking with the Orange Order for 40 years, said: "It really should not be contentious, this parade. Residents have made it contentions by appearing and protesting."
Politicians and PSNI Chief Constable Matt Baggott had appealed for calm ahead of the event, which was one of the biggest loyal order parades seen in Belfast.
The day culminated in a huge cultural festival staged in the grounds of Stormont to commemorate the 1912 proclamation against plans for Home Rule in Ireland.
The return feeder parade past St Patrick's passed off without incident.