It comes after more than 70 per cent of HES attractions opened again last month, including Edinburgh Castle and Fort George.
The latest roll-out of the phased reopening of sites will see Broch of Gurness on Orkney, Bonawe Iron Furnace in Argyll and Spynie Palace in Moray reopen their doors on May 24.
As Moray and Glasgow remain in Level 3 Covid restrictions, HES are advising visitors against travelling to or from these areas until the situation is again reviewed.
Dundrennan Abbey in Dumfries and Galloway and Edzell Castle in Angus will open their doors again to visitors on June 4.
Further sites, including Bothwell Castle in South Lanarkshire, Elcho Castle and Huntington Tower in Perth, Kildrummy Castle in Aberdeenshire and Maeshowe visitor centre on Orkney, will reopen on June 21.
The Maeshowe chambered tomb itself will remain closed due to space restrictions required under current Covid guidelines.
Visitors, however, will be able to enjoy an introductory talk highlighting Orkney’s heritage, interpretation of Maeshowe tomb and its world heritage Ranger base, as well as the on-site facilities and shop.
These sites will then be followed on June 30 with the addition of Dumbarton Castle and Rothsay Castle, with more ticketed sites set to reopen across the remainder of the summer.
Alex Paterson, Chief Executive of HES, said: “We are pleased to announce even more of our sites reopening up and down the country, providing visitors with the opportunity to enjoy much loved heritage attractions once again.
“We are opening a further 13 of our ticketed sites to visitors over May and June, including a number of seasonal sites, joining over 70% of our attractions which opened at the end of April with additional sites to follow.
“With over 5,000 years of history in our care, we’ve adopted a phased approach to reopening, providing as diverse a mix of attractions as possible, as well as reviewing and implementing the individual reopening requirements of each site, in line with Scottish Government guidance.
“We are now looking forward to welcoming visitors back to even more sites, providing further opportunity to enjoy Scotland’s diverse and globally renowned historic environment.”
As before, safety measures will be in place at all sites, with visitors wearing face coverings in indoor locations and in some enclosed spaces where social distancing can’t be easily maintained.
“There will also be initial capacity management on numbers and one-way systems will be in place in some locations.
“For the parts of several sites where access is currently restricted, a programme of agile interpretation has been developed which can be accessed via QR codes and includes digital film or audio to further enhance the visitor experience.”
Tickets should be booked online in advance from the HES website and are now on sale for the sites opening in May, with tickets coming online for June next month.
To book and for more information on further HES sites reopening, visit www.restarthistory.scot