In my view the following are the
best outward options (these times are for during the week):
(1) Depart Lime Street (Lower Level) at 10.13 (Merseyrail to Chester and change there onto Holyhead train)
13.50 Stena Line ferry from Holyhead to Dublin arr. 1705.
A bus will bring you from the ferry terminal door to Heuston Station.
18.15 Westport train departs Heuston. Arrive in Claremorris at 20.39.
(2) Depart Lime Street (Lower Level) at 07.55 (Merseyrail to Chester and change there onto Holyhead train)
11.50 Irish Ferries fast ferry from Holyhead arrive Dublin 13.39
Bus to Heuston.
14.45 train from Heuston to Claremorris. Arrive 17.14.
Best return options:
(1) Dep Claremorris 10.20, arriving Heuston 13.05
14.30 Irish Ferries fast ferry, arriving Holyhead 16.30.
(unfortunately the connecting bus departs Heuston at 13.00 and a taxi costs about €15. Might be possible to make the bus if the train arrives in a few minutes early. Sit in front carriage if possible to be nearest the exit at Heuston)
Trains depart Holyhead at 16.50 and 17.30.
Change at Chester.
Arrive in Lime Street at 19.43 or 20.13.
(2) Dep Claremorris 10.20, arriving Heuston 13.05
Taxi to port.
15.10 Stena Line ferry from Dublin, arriving Holyhead 18.40
Train departs Holyhead 19.21. Change at Chester and arrive Lime Street 22.13
Booking the ticket:
Online at Arriva Trains Wales. Has a section with lots of useful information too.
In person at staffed railway stations e.g. travel centre at Lime Street (the one in the main station) and local Merseyrail stations.
Children under 5 go free. 5-15 inclusive are charged half the adult fare. Return fare double the single fare.
No obligation to travel both ways with the same ferry operator. If wishing to travel out and back with different ferry operators just buy a Liverpool to Claremorris single over there and buy a single here for the return journey.
Claremorris station sells the tickets.
Buy a few days ahead.
Other information:
The bus fare from Dublin Port to Heuston station is not included in the SailRail ticket. Fare payable to driver.
Rail station and ferry terminal are side by side at Holyhead. There's toilets and a combined WH Smith-café too.
All the information may seem a bit daunting but it's straighforward enough and there'll be staff around at the various stations/ at terminal/ onboard ship to answer any questions about the journey.